Divisibility

problem
Favourite

What an Odd Fact(or)

Age

11 to 14

Challenge level

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
problem

Missing Digit

Age

11 to 14

Challenge level

What digit must replace the star to make the number a multiple of 11?
problem

There's Always One Isn't There

Age

14 to 16

Challenge level

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
problem
Favourite

Share Bears

Age

5 to 7

Challenge level

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
problem
Favourite

Statement Snap

Age

7 to 11

Challenge level

You'll need to know your number properties to win a game of Statement Snap...
problem
Favourite

Division Rules

Age

7 to 11

Challenge level

This challenge encourages you to explore dividing a three-digit number by a single-digit number.
problem

Book Codes

Age

7 to 11

Challenge level

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
problem
Favourite

Neighbours

Age

7 to 11

Challenge level

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
problem

Gran, How Old Are You?

Age

7 to 11

Challenge level

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
problem
Favourite

Curious Number

Age

7 to 11

Challenge level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?