Place value

problem
Favourite

Number Rules - OK

Age

14 to 16

Challenge level

2 out of 3

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

Double Digit

Age

11 to 14

Challenge level

1 out of 3

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

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?
problem

Alphabet Soup

Age

11 to 14

Challenge level

1 out of 3

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

Balance Power

Age

11 to 18

Challenge level

1 out of 3

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?