Place value

problem

Just Repeat

Age

11 to 14

Challenge level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
problem

Three Times Seven

Age

11 to 14

Challenge level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
problem

Composite Notions

Age

14 to 16

Challenge level

A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
problem

What Number?

Age

5 to 7

Challenge level

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.
problem

One of Thirty-Six

Age

5 to 7

Challenge level

Can you find the chosen number from the grid using the clues?
game

Dicey Operations in Line for Two

Age

7 to 11

Challenge level

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
game

Calculator Bingo

Age

7 to 11

Challenge level

This is a game for two players. What must you subtract to remove the rolled digit from your number? The first to zero wins!
problem

Six Is the Sum

Age

7 to 11

Challenge level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
problem

Napier's Bones

Age

7 to 11

Challenge level

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
problem

ABC

Age

7 to 11

Challenge level

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?