Place value

problem
Favourite

Always a Multiple?

Age

11 to 14

Challenge level

2 out of 3

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Favourite

Reversals

Age

11 to 14

Challenge level

2 out of 3

Where should you start, if you want to finish back where you started?
problem
Favourite

How Many Miles to Go?

Age

11 to 14

Challenge level

3 out of 3

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
problem
Favourite

Plus Minus

Age

14 to 16

Challenge level

2 out of 3

Can you explain the surprising results Jo found when she calculated the difference between square numbers?
problem
Favourite

Latin Numbers

Age

14 to 16

Challenge level

3 out of 3

Can you create a Latin Square from multiples of a six digit number?
problem
Favourite

2-Digit Square

Age

14 to 16

Challenge level

3 out of 3

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
problem
Favourite

Sixty-Seven Squared

Age

16 to 18

Challenge level

1 out of 3

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
problem

Purr-Fection

Age

16 to 18

Challenge level

1 out of 3

What is the smallest perfect square that ends with the four digits 9009?
problem

Novemberish

Age

14 to 16

Challenge level

1 out of 3

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.
problem

Lesser Digits

Age

11 to 14

Challenge level

1 out of 3

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?