Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
A game that tests your understanding of remainders.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Can you replace the letters with numbers? Is there only one solution in each case?
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Find the highest power of 11 that will divide into 1000! exactly.
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Can you work out what a ziffle is on the planet Zargon?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Here is a chance to play a version of the classic Countdown Game.
Given the products of adjacent cells, can you complete this Sudoku?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Can you find what the last two digits of the number $4^{1999}$ are?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
Can you complete this jigsaw of the multiplication square?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!