# Count On

## Explorer

#### Puzzle of the Day

These puzzles are also printed in Eight days a week, a booklet published by the Association of Teachers of Mathematics.

What is the smallest number (bigger than 1!) that will leave a remainder of 1 when divided by any of 2, 3, 4, 5, or 6?

Use three twos in three different ways so the second answer is twice the first answer and half the third answer. You can put add, take, times or divide between the twos. e.g. 2÷2+2=3

At what time on what day is it 2000 hours after the start of the Year 2000?

A man and his daughter have the same digits in their ages but in reverse. A year ago he was twice as old as her. How old are they now?

In a group of twelve elephants some are 9 years old and some are 11 years old. The total of their ages is 122 years . How many are aged nine?

Which 2 digit number has its digits reversed when you double it and take 1?

How many letters are there in the correct one word answer to this question?

Write a number as a word. Now write how many letters it has. Now write how many letters this has and so on. e.g. sixteen, seven, five, four, four, ... .Try other numbers and see what happens.

Which is the smallest number that you cannot score with 3 darts which all hit the dartboard (other than 1 and 2)?

If you had a set of ten cards numbered 0 to 9, could you make six numbers which are all multiples of three? (This means numbers like 3, 6, 78, 105 etc. which are something multiplied by three.)

Small oranges cost 8p each, large oranges cost 13p each. Some oranges are bought and the bill is exactly £1.00. How many of each size of oranges are bought ?

The chances of winning the lottery with 6 correct numbers is the same as naming a particular second from a period of 4 months. Is this true?

How many numbers between 10 and 99 inclusive contain different digits? (For example 36 has different digits but 33 doesn't.)

How can you use four of the digit 9 and any of +, -, x and ÷ to make 100?

Put three coins on a table all showing heads. Is it possible to make them all tails by turning two at a time? Try different numbers of coins.

The answer is 42. What is the question?

How many different ways are there to give someone 20p?

Can you find a two digit number that is 10 times as big as the two digits added together?

To change a temperature from degrees Celsius to Fahrenheit you can multiply by 9, divide by 5 then add 32. An approximate method is to simply double and add 30. For what range of temperatures is the approximate method within one degree of the accurate method?

If you write all the numbers from 1 to 100 how many times will you have written the digit 1?

Start with a three-digit number and repeat the digits to make a six-digit number, for instance 379379. Now divide by 7, then divide the answer by 11 and then divide this answer by 13. What do you notice? Does it always happen?

The average heart beats 70 times in a minute. How many beats in a leap year.

At the kick-off in a football match how many ones in total appear on the shirts of the two teams on the pitch?

A triangle has sides of 1cm, 2cm and 3cm. What is the area?

Start with any number and if it is even halve it but if it is odd add one. Now if this number is even halve it, if odd add one, and so on. Write each number down until you get to one. For instance 27 (add 1), 28 (halve it), 14 (halve it), 7 (add 1),8 (halve it), 4 (halve it), 2 (halve it),1 (stop). Which start number has the longest chain of numbers?

Draw a clock face with the numbers 1 to 12 in their usual positions. Can you draw a line so that the numbers on one side of it add up to five times the numbers on the other side?

Find a number whose double exceeds its half by 99.

I have 36p in 2p, 5p and 10p coins. If there are 7 coins altogether how many of each do I have?

A man was asked his age. I am 35, not counting Saturdays and Sundays, he replied. How old was he?

On a calculator 1 ÷ 3 is 0.33333333. What other numbers end in .33333333 when you divide by 3?

How many numbers between 1 and 100 do not have a 9 in them?

What is the largest possible number of people at a party if no two of them have their birthdays in the same month?

The average adult reads 300 words in a minute. About how long would it take to read a newspaper at that speed of reading?

How many different ways can you make 50p using 5p, 10p or 20p coins?

10 men dig 10 holes in 10 hours how long will 20 men take to dig 20 holes?

Write any three-digit number whose first digit differs from its last by 1. For instance 627 or 506. Reverse the digits then subtract the smaller from the larger number. Do this with several numbers. What do you notice? Does this always happen?

If you piled up a million pound coins about how high would it be?

How many pets do I have? All except four are dogs, all except four are cats and all except four are hamsters?

Make a number according to these clues:- (a) The digit 5 is three places before the digit 9 (b) The digit 3 comes before the digit 9, but after the digit 8 (c) The digit 4 is three places before the digit 3.

DIX is French for ten but what does DIX represent in Roman numerals?

Is it possible to find a five-digit number which has its digits reversed when it is multiplied by 9?

This is a game you can play on your own or with others. Choose any two digit number then write any four digits. See how close you can get to your chosen number using only the four digits with add, take, times or divide between them. Score 10 for direct hit, score 7 if within 2 of the target, score 3 if within 5 of the target.

At what time and on what day is it 2000 days after the start of the Year 2000

Draw five squares joined in the shape of a cross. Place digits (other than 0 or 1) so that the three numbers in the vertical line multiply together to give the same answer as the three numbers in the horizontal line mutiplied together?

If I could save £10 each week about how long would it take me to save £1 million?

What is the maximum number of Fridays you can have in one year (without travelling across a date line!)

Is it true that your height is roughly three times the distance around your head?

How many millimetres in a kilometre?

If letter \"a\" costs 1p,\" b\" costs 2p and so on, \"z\" costs 26p, can you find a word that costs £1?

Start at 80. You are allowed to add 11 and take 7 as many times as you like. Can you make 70? Try some other starts and finishes of your own. Is it always possible to finish where you choose from any start?

How long is a million minutes in weeks?

Make 3 two digit numbers and 1 single digit number using 1, 2, 3, 4, 5, 6, 7 and add them together to make 100.

On a calculator if you are allowed to use the \"4\" key and any of the add, take, multiply, divide and equals keys as many times as you like, what is the fewest number of presses needed to make 9 on the calculator? Set yourselves other targets and see how few presses are needed.

A light flashes every six minutes and a bell rings every eight minutes. If the light flashes as the bell is ringing, how long will it be until this happens again?

Using only 2p and 5p coins what amounts of money can not be made?

A wheel has ten spokes. How many spaces does it have between the spokes?

On a calculator try multiplying a number by itself several times and write down the answers. For instance 7 x 7 = 49, 7 x7 x 7 = 343, continue until you see a pattern in the last digit of the answer. If 7 was written 100 times with multiplication signs between them can you predict what the answer would end in?

Start with any number less than 20. If the number is even, halve it. If the number is odd, add one. Continue using the same rules writing each number one after the other. e.g. 17, 18, 9, 10, 5, 6, 3, 4, 2, 1. Do they always end in 1? What is the longest list of numbers?

If two dice are thrown what is the most likely difference between the two numbers ?

Using any combination of +, x, -, ÷ and all of the digits 2, 3, 6 and 8 once only, make the number 36.

About how long do you think it would take you to count to a million?

If you wrote all the numbers from 0 to 600, how many times would the digit 0 appear?

I am 48 years, 48 months, 48 weeks, 48 days and 48 hours old. How old am I to the nearest year?

What's next? 1, 4, 9, 16, ...

If I multiply the three digits on car number plates together what number am I most likely to get? (e.g. 377, 737, 773 are the only plates to give 147 but 234, 243, 324, 342, 423, 432, 146, 138, etc all give 24)

How many different ways are there to give someone 10p?

How long is a million hours in years?

A cage contained monkeys, giraffes and llamas. All but two of the animals were monkeys, all but two were giraffes and all but two were llamas. How many animals of each kind in the cage ?

Using any combination of +, x, -, ÷ and all of 2, 5, 7 and 9 once only, make the number 36.

Which is the greater: the number of metres in a kilometer or the number of Sundays in the next 20 years?

Thirty equally spaced points on the circumference of a circle are labelled in order with the numbers 1 to 30. Which number is diametrically opposite to 7?

This is a game for two. Start by writing zero. The first player adds 1, 2, or 10 and writes the answer. The second player adds 1, 2, or 10 to this answer and writes the new number, and so on. The winner is the first to reach 20.

How many squares are on a chessboard? More than 64! (Think of squares made up of smaller squares)

Using each of the digits 1, 3, 4, 8 once and once only it is possible to make 24 four digit numbers. Find the two numbers that are divisible by 4 and not divisible by 8 or 16.

How many days is a million seconds ?

Find a two-digit number so that when the digits are added together the answer is one half of the answer you get when the 2 digits are multiplied together.

If you are only allowed to press the 1 and 0 keys on a calculator with any of the add, take, times, divide and equals keys, what is the fewest number of presses needed to make the number 9 on the calculator? Set yourself other targets and see how few presses are needed.

At six o'clock a clock struck six times, the time between the first and last strokes being thirty seconds. How long will the clock take to strike twelve?

Which fruit is one third of a cherry and two fifths of an apple?

Using a standard pack of playing cards which is more likely when you are dealt one card: a card that divides by 3 or a picture card?

Exactly one of these numbered statements is true: 1. One of these statements is false. 2. Two of these statements are false. 3. Three of these statements are false. 4. Four of these statements are false. 5. Five of these statements are false. Which of the statements is true?

10:02:2001 will be the first palindromic date this millennium. (It reads the same both ways). How many more palindromic dates will there be this century?

As I was going to St. Ives I met a man with seven wives. Every wife had seven sacks. Each sack had seven cats. Each cat had seven kits. Kits, cats, sacks and wives, how many were going to St. Ives?

At what time on what day is it half way through the year 2000?

When asked for the sum of two numbers one person said 23 and the other said 210. They were both wrong because they had correctly done the wrong calculation. What were the numbers and what had each done?

Which two-digit number has its digits reversed when you double it and add 2?

How many minutes are there in the year 2000?

I have two coins totalling 55 pence. One of the coins is not a 50p piece. What are the two coins?

Split the number 17 into whole numbers (for instance 2 and 15 or 3, 4, and 10). Multiply these numbers together. What is the highest number that can be made ?

How many numbers divide exactly into 2000 ?

On a train there was 1 first class carriage, 1 buffet carriage and 4 second class carriages. In how many different ways can they be arranged if the second class carriages must be next to each other?

In a rectangular dance hall, how do you place ten chairs along the walls so that there are an equal number of chairs along each wall?

Three different numbers written on cards are placed side by side. The first and the second add up to 15. The second and third add up to 17. No card is a 7, or is higher than 9. Write down the 3 numbers in order.

How much would you need to be paid each callendar month if you were to be paid £1million over 40 years

Amanda has two children that aren't both boys. What is the probability that both children are girls? Bethan has two children and the eldest is a boy. What is the probability that both her children are boys?

What is a dozen plus a score plus a gross?

If I saved 1p on the 1st January, 2p on the 2nd, 4p on the 3rd, 8p on the 4th, and so on, how much money would I have saved by the end of the month of January? Answer in pounds.

How many seconds have you lived?

Using the digits 1, 2, 3, 4, 5 and 6 once each and two multiplication signs anywhere you like what is the largest number possible ?

Find amounts of money that can be made up in two ways so that one set of coins has twice as many coins as the other (but not using only 1p and 2p coins). e.g. 71p is 50p, 20p, 1p (3 coins) or 20p, 20p, 20p, 5p, 5p, 1p (6 coins)

What is the smallest number which is divide exactly by each of 1, 2, 3, 4, 5 and 6 ?

The digits of the year 1999 added together make 28. When will the digits of the year first be higher than 28?

Can you make 100 using five ones? You can put some of the digits together for instance 111 and you can use add, take, times or divide and brackets. Try using more or less than 5 of them and try other digits.

A doctor gives you three pills with the instruction take one every half hour. How long will they last?

Ahmed said Delia did it, Delia said Bruce did it, Bruce said Clare did it, Clare said she didn't do it and Eldon confessed that he did do it. If Ahmed didn't do it, one of the 5 did do it and if only one of them is telling the truth, who did it?

If I save 1p today, 2p tomorrow, 4p the next day and so on, doubling each day. How much will I have at the end of two weeks?

How many times does the digit 9 appear in all the numbers from 1 to 1000?

When will it be halfway through the first decade of this millennium?

Six children sit round a round table. Ahmed is two along from Davina, who is sitting next to Fred, on his left. Also two along from Davina sits Brenda, next to whom is Chris. Ahmed has Chris on one side and Ebenezer on the other. Describe how they are sitting.

The average heart beats 70 times in a minute. How many beats in a day.

A clock is set correctly at 1pm. It loses three minutes every hour. What will the clock read when the correct time is l0am the next day?

If you had a set of ten cards numbered 0 to 9 could you make five two-digit numbers which are all even?

Suppose someone is paid £20,000 in the year 2000 and each year afterwards is given a pay rise of 10% of the previous year's salary. In what year would they be paid £100,000? When would they have been paid £1 million in total? Try this for 5% increases.

If I have less than £1 in coins, what is the largest amount of money I could have and not be able to give someone exactly 50p?

Using four straight cuts what is the maximum number of pieces that a circular apple pie can be cut into?

How old is someone who has lived half a million hours?

When my mother was 40 I was 16. Now she is twice as old as I am. How old am I?

If you wrote the numbers from 1 to 99 what would all the digits add up to?

There are 101 spots on two Dalmatian dogs. One Dalmatian has 25 spots more than the other, how many spots does each have?

By changing only one letter turn the following words into words with a mathematical meaning: CORE, AUDITION, ATTITUDE, ECLIPSE, SQUIRE, TIN, SEVER, FINE

Below are some girls and boys first names. They are in code. Each digit always stands for the same letter. Try and work out the names: 900 340 323 1277 123415 890 464 What does 31890 stands for?

Using the digits 1, 2, 3, 4 and 5 and one multiplication sign anywhere you like what is the largest number possible ?

Approximately how many seconds old are you: 4 million, 40 million, 400 million or 4000 million?

One home improvement saves 30% on fuel, a second saves 45% and a third 25%. If you use all three can you save 100%. If not why not?

I picked a bunch of flowers. All but 6 were white, all but 6 were blue, all but 6 were yellow. How many flowers in the bunch?

What is the next palindromic number after 72927? (A palindromic number reads the same forward and backward)

If four letters are put into four envelopes at random, what is the probability that only three of the letters are put into the correct envelopes?

How \"fair\" are the coins in your pocket? Try flipping a coin 50 times and counting the number of heads. Try this several times. Do you always get the same?

What's next? A) 3, 3, 5, 4, 4, 3, 5 ..., B) O, T, T, F, F, S, S, ... (HINT - they are related)

What is the number if its units digit is 4 more than its tens digit and its units and tens digits add up to 10

Try these on a calculator then predict what the next in the pattern will be when your calculator display is not big enough. 11 x11, 111 x 111, 1111 x 1111, etc.

Using the digits of 1999 kept in that order and the operations +, -, x, ÷, and brackets can you make any of the numbers from 1 to 20? (For example 9 is 1x(9+9)-9

13 x 13 = 169 and 31 x 31 = 961. Can you find other numbers which give answers in reverse order when they are reversed and multiplied by themselves?

If you wrote all the numbers from 0 to 600, how many times would the digit 5 appear?

Three consecutive numbers multiplied together give 3360, what are the numbers ?

Which number is this? It has 2 digits, it is prime and it is 2 more than a square number. (You make a square number when you multiply something by itself, so 49 is square because it is 7 times 7. A prime number only divides by itself so 2, 3, 5, 7, 11 etc. are primes.)

A snail crawls up a 2m fence post. He crawls up 30 cm every hour but then rests and slips back 10 cm. How long will it take him to reach the top?

What mathematical symbol can we place between 2 and 3 to make a number greater than 2 and less than 3?

A water lily in a pond doubles its size every day and in 28 days it fills the whole pond. How long does it take to fill half the pond?

A certain number between 700 and 900, gives a remainder of 1 each time when divided by 2, 3, 4, 5, 6, 7 and 8. What is the number ?

472 + 274 = 746. The digits of 472 have been reversed and added to it. Can you find other ways to make 746 using a number and its reverse?

Draw a square then draw a square on each of its sides. Which 5 different numbers from 0 to 9 can be put in the squares so that the 4 outside numbers add up to the middle number?

How long would it take to you write all the numbers from one to 2000?

What is the number if it is 1 less than a square number and it is not divisible by 3 or 7 (You make a square number when you multiply something by itself, so 49 is square because it is 7 times 7)

One painter can paint a wall in 30 minutes, another painter needs 15 minutes for the same size wall. How long will they take to paint the wall working together?

Which is most likely, two coins both landing heads up or a picture card being chosen at random from a full deck?

There are six combinations of numbers possible using the digits 2, 3, 8. How many of these combinations are even?

How many different numbers can you make if you use the digits 1, 2, 3, 4 once each, in any order, and a times sign. For instance 31x24, or 2x413.

If you have to finish with a double in a game of darts, which number has the most number of different ways of finishing with 2 darts? (for instance 20 could be 18 and double 1, double 8 and double 2, treble 2 and double 7 etc )

If I save 5p today, 10p tomorrow, 15p the next day and so on, 5p more each day. How much will I have at the end of two weeks?

The numbers on five houses next to each other add up to 55. What can they be?

A BBC commentator once spoke 176 words in 30 seconds. How many words could he have spoken in describing a 100m race. How would you compare?

In a village there are 800 women. 3% of them wear one earring. Of the other 97% half are wearing no earrings and half are wearing two. How many earrings altogether are being worn by the women?

Are there more seconds in a year or hours in a century?

Use five twos and as many plus signs as you need to make 28

What is the largest value you cannot make with an unlimited supply of 13p and 6p stamps ?

Which number am I describing ? It is palindromic (i.e. reads the same backwards as forwards). It is an odd number, it is a cube number, it is a multiple of 7, two more than it is divisible by 5 and it has 3 digits. (A cube number is like 125 which is 5x5x5 or 27 which is 3x3x3)

Five parcels labelled A, B, C, D and E weigh 60 kg. When arranged in a certain order, each weighs 1kg heavier than the one before it. E is 1kg heavier than A which is 2kg lighter than B. D is 1 kg lighter than C, which is 3 kg heavier than E. Write down the order.

A boy has as many brothers as sisters but his sister has only half as many sisters as brothers. How many boys and how many girls are there in the family?

A first class stamp costs 26p, a second class stamp costs 21p. I buy some stamps and the cost is £1.93. How many of each price have I bought?

What is the only whole number between one and ten which does not divide exactly into 360?

A secret code has the word BACON coded as 3, 2, 4, 16, 15. What would be the code for EGGS?

What is the number if it has 3 digits (all different) and each digit is 3 times the one before?

A golf player can only hit shots of two lengths. On the first nine holes of a course the player hits balls 150yds, 300yds, 250yds, 325yds, 275yds, 350yds, 225yds, 400yds and 425yds. What are the lengths of the two shots?

Using all the digits from 1 to 6 once only, make three two-digit numbers which multiplied together give the smallest number possible.

Draw a clock face with the numbers 1 to 12 in their usual positions. Can you draw a line so that the numbers on one side of it add up to twice the numbers on the other side?

A fish weighs 10kg plus half its weight. How much does it weigh?

Estimate how far you walk in a day.

A street of houses numbered from 1 to 100 inclusive is to be numbered with new brass numerals. How many of the digit \"2\" would be needed to complete the job?

How is it possible for four birds to position themselves so that each is the same distance from the other three?

Two ducks in front of a duck, two ducks behind a duck and a duck in the middle. What is the fewest number of ducks?

23 x 64 gives the same answer as 46 x 32 (everything written in reverse order) can you find other pairs of two digit numbers with different digits that work like this?

Which number, less than 100, is increased by one fifth when its digits are reversed?

If there are ten blue socks, ten red socks and ten brown socks in a drawer in a dark room how many socks must be removed to ensure they contain: (a) a matching pair? (b) a blue pair?

625 is a square number because it is 25 times 25 (a number times itself). Find two square numbers, each of which uses all three digits 1, 9 and 6.

You have some rabbits and pigeons. In total there are 7 heads and 18 legs. How many rabbits do you have?

Over a period of time a friend and I played 211 games of pool. I won 25 more than I lost and there were no draws. How many did I win and how many did I lose ?

What is the smallest possible number of children in a family if each child has at least one brother and at least one sister?

In the English language what is the smallest whole number which contains the letter \"a\"?

Find a five-digit number which has it's digits reversed when it is multiplied by 4.

Using all the digits from 1 to 5 once only, make two numbers which multiplied together give the smallest number possible.

How many times in 24 hours are the hands of a clock at right angles to one another?

A family of 5 girls, all of different ages, share £1000 so each receives £20 more than her next younger sister. How much does the youngest receive?

Using any combination of +, -, x, ÷ and all of 1, 3, 3, 5 once only, make the number 36.

Two reds and all the colours are left on a snooker table? How many points are available?

What is the number if it is 9 more than its reverse and the sum of the digits is 11 (the reverse of a number just means write it in reverse so 724 is the reverse of 427)

A girl walks 2 miles north, then east for 3 miles, south for 3 miles, west for 2 miles and north for 1 mile. In which direction and how far should she walk to return to the start ?

Arrange all the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to give four different square numbers. (You make a square number when you multiply something by itself, so 49 is square because it is 7 times 7)

If A and I stand for two even numbers and L and B stand for two of the operations +, -, x, ÷, can you make ALIBABA = 40?

What is the smallest number of eggs that could be shared equally by 2, 3, 4 or 5 people with 1 being left over each time ?

If you reverse the digits of Alan's age it is the same as Brian's age. The difference between their ages is twice Carol's age and Brian is 10 times as old as Carol. What are their ages? (You might need a fraction)

If you are given change for £1 in 5p and 10p pieces, and you get 1 more 10p than 5p, how many of each are there ?

Estimate how many times you breathe in a year.

A newspaper is made up of double spread sheets. Page 13 was missing and the back page was page 20, which other page numbers were missing?

Which is most likely, a letter chosen at random from the alphabet being a vowel or throwing a six on a dice?

Draw a triangle. Write one of the numbers from 1 to 6 at each corner and one of the numbers along each side (no repeats). Can you arrange them so each side adds up to the same number?

Using all the numbers from 1 to 10, put them into pairs, so that four pairs add up to 12 and the final pair adds up to 7.

Which 2 digit numbers become 27 bigger when the digits are reversed ?

Using all the numbers from 1 to 10, put them into pairs, so that one pair adds to 6, another pair to 7, a third pair to 9, a fourth pair to 16 and the final pair add to 17.

On average you inhale about 0.6 of a litre of air in one breath (that's about a pint). Estimate how much air you breath in a day.

The three-toed sloth moves at about 2 metres per minute how long would it take to travel a mile?

Using the usual coins in circulation how many ways can you make 6p?

What number gives the same result if you divide it by 2 or take 2 from it? What number gives the same result if you divide it by 3 or take 3 from it? (Hint: you will need to include a fraction or decimal for this one).

A cubic metre of water weighs 1 tonne. Estimate the weight of water in a swimming pool.

I drink about six cups of tea or coffee each day and that is about three pounds in weight. If I weigh 12 stone in how many days do I drink my weight in tea and coffee? (There are 14 pounds in one stone)

What is the biggest number you can find in a kitchen?

If a letter \"a\" costs 1p,\"b\" costs 2p and so on, \"z\" costs 26p, can you find a word that costs 50p

How many different numbers can you make using only the digits 1, 2, 3, 4 and an add sign.? For instance 31+24, or 1+243.

Ask some one to pick a number from 1 to 1000. You are allowed to ask ten questions to find the number which they can answer yes or no. What should you ask?

The digits of the year 1999 added up to 28. When is the next time the digits of the year will add up to 28? When else will it happen?

Which is worth the most, a kilogram of 1p coins or a half kilogram of 2p coins?

Write the numbers :- 3, 4, 5, 6, 10, 12, 13, 15 in a different order, so that numbers next to each other add to give square numbers. (You make a square number when you multiply something by itself, so 49 is square because it is 7 times 7)

In an election 39,218 votes were cast for two candidates. The winner had 1002 votes more than the loser. How many votes did they each receive?

What is the biggest number you can find on a car?

Start with any two-digit number. Multiply each digit by itself then add these answers. Do the same thing to this new number and so on until something happens. For example 32 becomes 9+4 which is 13, 13 becomes 1+9 which is 10, 10 becomes 1+0 =1. This one ends at 1. What else happens when you start with different numbers?

Using the digits 1, 2, 3, 4, 5, 6 make two three-digit numbers and multiply them together. What is the biggest answer you can get?

How many pages would a book contain if it had a million words?

In a kitchen there are 11 cupboards some with one door and some with two. There are 15 doors altogether so how many of each cupboard are there?

Find the number that when added to its reverse is closest to 50. Try this for 100, 150, 200, 250. For instance 122+221 is the closest to 350.

Dominoes have 0, 1, 2, 3, 4, 5, or 6 spots on each end and there is only one domino for each possible combination. How many dominoes are there in a normal set of dominoes?

How many square inches in a square foot?

Where are there numbers in your house?

Start with two different numbers. Add them and then multiply them together. Does the first answer divide exactly into the second? e.g. 4+12=16 and 4x12=48. 48÷16=3. Find some more that work. What is special about pairs of numbers like this?

Using all the digits from 1 to 5 once only, make two numbers which multiplied together give the largest number possible.

What number is represented by LIX in Roman numerals?

A four-digit number is \"lucky\" if its digits add up to 6 and no digit is 0. Find all ten \"lucky\" numbers.

A horse weighs 600kg plus 1/3 of its weight. What does it weigh?

Goldbach's Conjecture claims that every even number greater than 2 is the sum of two primes. A number is a prime if it only divides by itself or 1. So 2, 3, 5, 7, 11, 13, 17, 19 etc. are primes. Think of an even number and find two primes which add together to make your number. For instance 8 is 3+5 and 22 is 11+11. Can you find one that doesn't work?

On which date is the hundredth day of the year 2000?

The first odd number is 1. What is the hundredth?

How many ways can a car measure things?

The numbers 1, 2 and 3 have been placed at the corners of a triangle. Arrange the numbers 4, 5, 6, 7, 8, and 9 on the sides, so that the numbers along each side (including the corners) add up to 17.

The digits of the year 2000 add up to 2, 2001 add up to 3, 2002 add up to 4 but this will also happen in 2011. Find all the years when the digits add up to 4, 5, ...

Put 6 dominoes in a 3 by 2 rectangle arrangement. How many rectangles are formed within the whole shape?

The vowels have been taken out of some mathematical words. Can you work out the words: CB, RDS, DGNL, NGL, QLTRL, CN, CT, LGBR, VRG, RT, R ?

A man and his daughter together weigh 90kg, the man with his cat weigh 70kg, the daughter and cat together weigh 40 kg. What do they each weigh?

How many diamonds are there on playing cards in a 52 card pack? (This will vary depending on style)

Three dice are rolled and the scores are multiplied together. The product is 90. What were the scores on the three dice?

What numbers are considered lucky or unlucky and why?

What is the minimum number of each coin I need if it is to be possible for me to give any amount of money from 1p to 50p?

A market trader has 27 watches at the start of the day and after selling some he reduces the price by £5. He sells them all for £475. What was the original price?

Find a two digit number, so that when the digits are added together the answer is one third of the answer when the 2 digits are multiplied together.

The length of the Loch Ness monster is 20 metres long and half its own length, but it isn't 30 metres long. How many metres long is it?

Try these calculations: 1 x 9 + 2 = , 12 x 9 + 3 = , 123 x 9 + 4 =, ... continue the pattern and see if you can predict the answers before calculating.

A cricket chirps faster when the weather is warmer. The number of chirps per minute is approximately 7 times the temperature (in degrees Celsius) and then take 20°C. How fast would it chirp if the temperature was 30°C? What would the temperature need to be for it to chirp at 150 chirps per minute?

How much earth is there in a freshly dug hole that is 20cm deep, 15cm wide and 45cm long?

What is your favourite number and why?

Draw a triangle. Write one of the numbers from 1 to 6 at each corner and one of the numbers along each side (no repeats). Can you arrange them so each side adds up to 12?

If the final score in a football match was 3 - 2 how many different possible half time scores are there? For instance 1 - 0 or 0 - 1. Could you give a rule for working out how many half time scores there are just using the final score?

When Christine is twice as old as she is now, she will be three times as old as she was three years ago. How old is Christine now?

Can you find four consecutive numbers which add up to 10?, 14?, 50?, 106? Is there a quick way to find them?

At what time on what day is it 2000 minutes after the start of the Year 2000

Can you work out your weight in kilograms if you know it in stones and pounds? You need to know that 1 pound is 0.454kg and that 14 pounds make a stone.

How many days from Christmas 1999 until Easter in 2000?

What is the most important number in your house, and why?

Start with a 2 digit number and multiply its digits together then multiply the digits of the new number together and continue until you get a single digit. For instance start with 39, do 3 times 9 to get 27, 2 times 7 gives 14 and 1 times 4 is 4. So 39 gives a chain of 4 numbers. Which start number has the longest chain?

The five consecutive numbers 1, 2, 3, 4, 5 added together come to 15. The three consecutive numbers 4, 5 and 6 also add to 15. There is one other way to add consecutive numbers to make 15. Can you find other numbers which can be made by adding several different sets of consecutive numbers?

2 x ABABAB = 9x BABABA. Can you find what A and B stand for in these six-digit numbers?

A chimney sweep has 7 rods - they are 5.1m, 4.5m, 2.7m, 2.1m, 1.2m, 0.9m, 0.6m. Which five rods will reach exactly to the top of a 12 metre chimney ?

The ages of three children added together come to 20 and when multiplied together make 280. If the ages are multiplied together in 10 years time what will the answer be?

Find three different whole numbers that add up to 10. How many different ways can this be done?

Can you work out your height in centimetres if you know it in feet and inches? You need to know that 1 inch is 2.54cm and that 12 inches make a foot.

It is raining at midnight. Will the sun be shining in 72 hours time?

We read the number 123456 as one hundred and twenty three thousand, four hundred and fifty six. How do we read the number 9876543210

When asked his age, a man replied that when it was divided by 2, 3, 4 or 6, there was one left over in each case. When his age was divided by 7 there was no remainder. How old was he?

I bought 2 pencils at 12p each and 5 pens at 24p each. I also bought 7 identical notebooks. I was told the total was £5. Why couldn't that be right?

Three numbers add up to 14. Multiplied together they come to 84. Find the numbers.

At a party 28 handshakes were exchanged. Each person shook hands exactly once with each of the others. How many people were present?

If I weigh 60kg what is my weight in stones and pounds? You need to know that 1 pound is 0.454kg and that 14 pounds make a stone.

In a code, if KZWNX means REACH, what does NWKZ mean ?

What pubs have numbers in their names?

On a digital clock there are times which have the special property that the minutes digits add up to the hours digit, like 7:25 or 13:49. Which hour has the most of these times?

If a letter \"a\" costs 1p,\" b\" costs 2p and so on, \"z\" costs 26p. What is the most expensive boy's name you can find?

How many different ways can you find to make a square out of 8 dominoes? (Don't worry about the spots - just think of the rectangle shape. Assume they are twice as long as they are wide.)

A pen and pencil cost £5. The pen costs £4 more than the pencil. What is the price of each?

The three consecutive numbers 5, 6, 7 add up to 18. Can you find three consecutive numbers which add up to 9?, 12?, 30?, 300? Is there a quick way to find them?

At what time on what day is it 2000 seconds after the start of the Year 2000?

Multiply the number of months with 31 days by the number of months with 30 days. What does this give you?

What places have numbers in their names? (e.g. Four Lanes in Cornwall)

Nine numbers between 3 and 180 cannot be obtained with three darts. Name one.

Using the digits 1, 2, 3, 4, 5, 6 make two three digit numbers and multiply them together. What is the smallest answer you can get?

Draw a clock face with the numbers 1 to 12 in their usual positions. Can you draw a line so that the numbers on one side of it add up to the same as the numbers on the other side?

Which are the only three whole numbers that when added together and multiplied together give the same answer ?

I am 48 and my wife is 39. How old was I when I was twice her age? How old was I when I was four times as old as her?

If a child is one metre tall what is their height in feet and inches? You need to know that 1 inch is 2.54cm and that 12 inches make a foot. What would a 2m person be in feet and inches?

The average heart pumps 4 litres (about 7 pints) of blood per minute. How many litres in a day? How many gallons? (A gallon is 8 pints)

If you turn a left handed glove inside-out will it be right handed or left handed?

An odd day is one which has both its day and month odd for instance 13:5:2000. How many odd days are there in the year?

In any day before noon how many times is the sum of the digits of the time equal to 15? For instance 2:58 and 11:49 are two times when this is true.

How many ways can you find to make the number 10, by adding or subtracting prime numbers? The same numbers but in a different order count as the same answer. (Prime numbers are only divisible by themselves and 1 so they are 2, 3, 5, 7, 11, 13, ...)

What's next? A) 31, 28, 31, 30, 31, 30... B) 7, 8, 5, 5, 3, 4, ... (HINT - they are related)

How long would it take you to count a million pounds?

There are three ways to make 12 by multiplying two whole numbers together 1 x 12, 2 x 6 and 3 x 4. Can you find numbers that have more than three different multiplications of two whole numbers?

If you have five cows, twelve hens and a goat. How many legs in total?

Bill and Ben are twins. Bill is 40. How old is Ben?

Start with a two-digit number, reverse the digits to make a new number then subtract the smaller from the larger number. Repeat this process until you reach a single digit. Start with other numbers. What do you notice? e.g. 82-28=54, 54-45=9

Find an estimate for how many bricks are needed to build a house.

How old is someone who has lived a million minutes?

Multiply together any four consecutive numbers (for instance 7,8,9,10) then add one. You should be able to find a number which when you multiply it by itself gives this same answer. Does this always work?

Once whilst they were growing up a girl's age in years was five times her brother's age, later it was four times then three times his age. Now her age is twice his age. How old are they both now?

Estimate what weight of liquid you drink in a year. A cup of tea or coffee is about half a pound, a pint weighs about a pound and a quarter, and a litre of wine or soft drink is about 2 pounds in weight.

In total, how many grandparents did your grandparents have?

How many different years are there? (e.g. Financial, Jewish etc.)

How many different positive numbers can you make using each of the digits 1, 2, 3, 4, once only, and a take away sign? For instance 31-24, or 413-2.

Can you make 2000 by adding up consecutive numbers?

A glass is full of milk. The total weight is 370g. When the glass is half full of milk, the weight is 290g. What is the weight of the glass?

Find four numbers so that the same answer is obtained when:- (a) 4 is added to the first (b) 4 is subtracted from the second (c) the third is multiplied by 4 (d) the fourth is divided by 4. One last clue - they add up to 75.

If exactly £3.90 was spent on some 24p and some 18p stamps, how many of each are there? (There is more than one answer)

Can you divide a clock face into three parts so that the hour numbers in each part add up to the same?

If November 5th falls on a Saturday on which day will Christmas day fall?

After a cyclist has gone two thirds of his route he gets a puncture. Finishing on foot, he spends twice as long walking as he did riding. How many times as fast does he ride as walk?

If I do something with 2 and 3 I get 11, if I do the same thing with 3 and 4 I get 19, the same thing again to 3 and 7 gives 52. What would I get if I do the same with 4 and 5?

If the average heart pumps 4 litres of blood per minute, how many litres does it pump in a year?

Three days ago, yesterday was the day before Sunday. What day will it be tomorrow?

Find two 3 digit square numbers that are the reverse of each other ? (Remember 256 is a square number because it is a number multiplied by itself, 16x16)

Using the digits 1, 2, 3, 4 and 5 once only, one multiplication sign and one division sign anywhere you like what is the smallest whole number you can make ?

If the two digits of a two digit number are reversed it is 45 more than it is now. What could it be?

Five yeast cells were placed in a laboratory dish at 2pm. The number of yeast cells doubles in every ten minute interval. What is the number of yeast cells in the dish at 3pm?

In English which is the smallest positive whole number which requires four syllables to pronounce it?

There are 24 possible numbers using all the digits 2, 3, 4, 5. How many of these are odd numbers?

If 125g (about a quarter pound) of tea makes a hundred cups what weight is needed for a million cups?

The names of the numbers from one to twelve are written down in alphabetical order. What is the fourth number on the list?

Can you find a two digit number that is twice as big as the two digits multiplied together?

Find three different whole numbers that add up to 20. How many different ways can this be done? (The order they are written is not important

What time and day will it be 100 hours from now?

When was the last year which reads the same upside down?

A ship leaves port and when it is 180 miles from shore a seaplane which flies ten times as fast as the ship follows it. How far from shore does the plane catch up with the ship?

What is the number if it divides exactly by 13 and when you write its digits in reverse order you make a square number. (You get a square number when you multiply a number by itself - 64 is square because it is 8 times 8)

If you have 7 sticks which measure 1cm, 2cm, 3cm, 4cm, 5cm, 6cm, and 7cm is it possible to make two lines of the same length with them? Can you make four lines of the same length?

A brass band of 40 musicians takes 4 minutes to play a march. How long would a band of 60 musicians take?

Put the numbers 7, 8 and 9 at the corners of a triangle. Can you place the numbers 1, 2, 3, 4, 5, 6, in twos on each side to make the same total on all three sides (include the numbers at the corners)?

What numbers can you make using each of the digits 1, 2 and 3 (once only) with any add, take, times or divide signs? For example 1x2x3 or 3-2÷1

How many triangles are there in a regular pentagon with all its diagonals drawn? (a regular pentagon has five straight sides all of the same length and five equal angles. A diagonal is a line joining points.)

Bessie Biker rides to her friends at 30 mph and back at 20 mph. What is her average speed for the round trip?

What two whole numbers multiplied together make 1 million if neither of them have any zeros?

What is the number if it divides by 3 and it is 3 less than a number that divides by 10. (There can be more than one answer!)

If we add 12 thousand, 12 hundred and 12 what is the largest digit in the answer?

What is the most and the fewest Sundays you can have in a year?

Can you find a two digit number that is three times as big as the two digits multiplied together?

A knockout competition has 60 teams entering. How many matches need to be played? (Some teams will need to have byes)

One year in the new millennium when Julie multiplies her age by itself the answer will be the same as the year. In what year was she born?

Two farmers are on their way to market to sell their sheep. One says to the other \"Sell me one of your sheep and then we will have the same number\" to which the other replies, \"No, you sell me one of yours and then I will have twice as many as you\". How many sheep did each farmer have?

What is the number if it is in the 9 times table and it is 9 more than if its digits are reversed?

A collection of birds and beasts has between them 120 feet and 43 heads. How many birds and how many beasts?

How much longer than 52 weeks is a leap year?

This is a game for two. Start with a number between 11 and 19 and take turns to add a number between 11 and 19. The winner is the first to go over 100.

2 + 47 = 49, 2 x47 = 94 so the digits of the answer are the same but in reverse when you add or multiply 2 and 47. Can you find other pairs which have answers with digits reversed when added and multiplied?

The factors of 12 are 1, 2, 3, 4, 6, 12 because they all divide into it . What is the smallest number with three factors? What types of numbers 3have three factors?

Estimate your weight in packets of crisps.

On a long distance rally, Rosie Rallydriver drives at, on average, 60 mph and arrives an hour earlier than Susie Slowcoach who averages 50 mph. How long is the rally (in miles)?

If you could take a million paces about how far do you think you would you travel?

Try these on a calculator then predict what the next in the pattern will be when your calculator display is not big enough. 99 x 99, 999 x 999, 9999 x 9999, etc.

What is the number if: (a) it is square (b) one more than the number is a multiple of 10? (You make a square number when you multiply something by itself, so 36 is square because it is 6 times 6)

What is the probability that the next person you meet has an above average number of arms: Impossible, unlikely, evens, very likely or certain?

1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, etc. The numbers 1, 4, 9,16, 25, 36 etc. are called square numbers because you multiply a number by itself to find them. Can you make all the numbers from 2 to 100 by adding square numbers? e.g. 40 = 25 + 9 + 4 +1 +1.

Using all the digits from 1 to 6 once only, make two numbers which multiplied together give the largest number possible.

Find this five digit number. With a 1 after it, it is 3 times as large as it is with a 1 before it.

The distance around the equator is 40 000 km or approximately 25 000 miles. Estimate how long it would take to travel that distance.

Which two numbers (neither of which contains any zeros) multiply together to give 100?

To get to the store room Mandy had to go up a staircase of 21 steps, along a short passage and then down a staircase of 14 steps. How many more steps up than down did she take on the journey there and back ?

How many presents did my true love send to me over the 12 days of Christmas?

What numbers can you get on a calculator if you are only allowed to use the 3, 5, + and = keys?

What is the least number of coins needed to be able to make any amount of money from 1p to £1.

In a car park there are some motorbikes, cars and 8 wheeled lorries. If there are 4 handle bars, 44 wheels and 11 vehicles in total, how many of each ?

What links the number 7 with the digits 1, 2, 4, 5, 7, 8? (Hint: try using a calculator)

What is the number if the difference between the two digits is 3 and the number is square (If you have forgotten what a square number is: You make a square number when you multiply something by itself, so 49 is square because it is 7 times 7)

A triangular field has a tree in each corner and five trees along each side. How many trees altogether?

Have you ever measured yourself in centimetres? Are you good at estimating in centimetres? First estimate then check with a tape measure your height, your waist measurement, around your wrist, around your head. Are you any better at estimating in inches?

Draw a triangle and write a number between 1 and 9 at each corner. Now put the other six numbers in pairs on the sides. Is it possible to arrange them so that each line of four numbers adds up to 20?

In a chess league, each of the competitors plays each of the others once. If there are 300 games altogether, how many competitors?

Each girl in a family has the same number of sisters as brothers, but each boy has only half as many brothers as sisters. How many children are in the family?

I was 8 years old when my father was 31 . Now he is twice as old as I am. How old am I?

Estimate the value of a tonne of £1 coins.

How many spots are there altogether on five, normal, six - sided, dice ?

If you write down all the names of the numbers from 1 to 100 how many times will you write the letter L?

If you have difficulty remembering some times tables try making up some \"times rhymes\" for instance \"seven times seven is very fine because it equals 49\

How can you use six nines to make 100?

If letter \"a\" costs 1p,\" b\" costs 2p and so on, \"z\" costs 26p. What is the most expensive girls' name you can find?

If you have sticks which measure 1, 2, 3, 4, 5, 6, 7, 8 and 9 cm (one of each) how many different triangles could you make using three of the sticks?

The Product of two numbers is six times their sum, and the sum of their squares is 325. What are the two numbers? (You square a number if you multiply it by itself. Product means multiply together and sum means add together)

Enter 38 on a calculator. Now reduce it to 1 by using any operation key and the number 3 only. What is the fewest number of key presses needed?

The supermarket has a special offer on tins of cat food - buy 5 get one free. 10 tins cost £4.32. What would 20 tins cost?

Six stations lie at equal distances from each other along a railway line. How many times further is it from the first to the sixth than it is from the first to the third?

A boxing match has twelve rounds each of 3 minutes and there is a minute between each round. How long does the match last?

Make a number chain. Write any number (up to 40) and multiply its last digit by 4 then add its other digits to this. Write down the new number and repeat the process until you return to the original. For instance 7, 28, 34, 19, 37, 31, 7. What is the longest chain you can make?

Write down any three consecutive numbers. Multiply the first by the third and multiply the second by itself. Try some more. What do you notice?

Using the usual coins in circulation what is the smallest amount which cannot be made using fewer than four coins?

What is the smallest number that cannot be obtained with one throw of a dart?

1234 divided by 11 is not a whole number but if you rearrange the digits it is possible to find a number that divides by 11 to give a whole number. How many different ways can you find to do this?

How many days will there be this century? (Don't forget leap years.)

How thick is a piece of paper? Make a guess then find a way of working out the thickness.

A clock takes three seconds to strike 4 o'clock. How long will it take to strike 6 o'clock?

Write the numbers from 1 to 100 with either an add or subtract sign between each. Can you make the total 2000?

You are only allowed to use the 7, 3, x, - and = buttons on a calculator (as many times as you like). Try to make it display each of the numbers from 0 to 9.

Some boys and girls have £32 between them. Each boy has £4 and each girl £5. How many boys were there?

Two friends were working out how many sweets they had. One said I've got twice as many as you and if we eat one each I will have three times as many as you. How many did each have?

Using any combination of +, -, x, ÷ and all of 1, 3, 3, 5 once only, make the number 36.

On average you inhale about 0.6 of a litre of air in one breath (that's about a pint). Estimate how much air you breathe in a year.

What is the smallest even number which cannot be obtained when the scores on two dice are multiplied together? What is the largest odd number which can be obtained?

The year 1991 read the same backwards and forwards, when is the next year this will happen?

Can you make 1000 with eight eights? You can put some of the eights together for instance 88 and you can use add, take, multiply or divide and brackets.

A triangle with two equal sides is called an isosceles triangle. What isosceles triangles can you find that have sides with a total length of 59 cm? (Use only whole numbers of centimetres for each side)

A household has some goldfish, some canaries and some rabbits. Altogether there are 15 heads and 26 legs. How many of each animal could there be?

How many spots are there on a standard domino set?

I divided a whole number by another whole number and the answer was 0.4705882 on my eight-digit calculator display. They were both less than 20. Can you find them?

The reflection of a clock shows 3.55 (five to four), what time is it really ?

Think of a number, multiply it by 5 and add 3. I could find your number if you gave me the answer and I first took away 3 then divided by 5. It is always possible to find out the original number by reversing the steps, so try giving other people puzzles like this and work out what number they started with.

How can you get 101 with two darts?

Write two two-digit numbers whose digits add up to the same number. For example 56 and 29 (digits add up to 11) now take one from the other and add the digits of the answer. Do several pairs. What do you notice?

Estimate the weight of food you eat in a day. How much is that in a year?

Sometimes when you divide the day by the month you get a whole number, for instance 15th May gives 15 divided by 5 which is 3. How many days in a year give whole numbers.

One item costs £6 more than another. Two of each of them cost £22 in total. How much for each of the items ?

If my son gives my daughter 10p they will both have the same amount. If she gives him 10p he will have twice as much as her. How much do they have each?

If there are 5 Mondays, 5 Tuesdays and 5 Wednesdays in January, on which day of the week will February 1st fall?

How many times in a day does the hour and minute hands on a clock point in opposite directions?