Place value

problem
Favourite

Number Rules - OK

Age

14 to 16

Challenge level

Can you produce convincing arguments that a selection of statements about numbers are true?
problem
Favourite

Latin Numbers

Age

14 to 16

Challenge level

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

2-Digit Square

Age

14 to 16

Challenge level

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

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

Double Digit

Age

11 to 14

Challenge level

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?
problem

Purr-Fection

Age

16 to 18

Challenge level

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

Novemberish

Age

14 to 16

Challenge level

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

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

Alphabet Soup

Age

11 to 14

Challenge level

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.
problem

Multiplication Magic

Age

14 to 16

Challenge level

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.