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?
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?
Resources to support understanding of multiplication and division through playing with number.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Can you work out what a ziffle is on the planet Zargon?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Amazing as it may seem the three fives remaining in the following
`skeleton' are sufficient to reconstruct the entire long division
Given the products of adjacent cells, can you complete this Sudoku?
A game that tests your understanding of remainders.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Here is a chance to play a version of the classic Countdown Game.
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!?
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?
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?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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.
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Find the highest power of 11 that will divide into 1000! exactly.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Choose a symbol to put into the number sentence.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
If the answer's 2010, what could the question be?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the information to work out how many gifts there are in each
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.
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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 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. . . .
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" .
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?