Place value

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
Not a polite question

Age

11 to 14

Challenge level

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
problem
Legs eleven

Age

11 to 14

Challenge level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
problem
Big powers

Age

11 to 16

Challenge level

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
problem
Digit sum

Age

14 to 16

Challenge level

What is the sum of all the digits in all the integers from one to one million?
problem
Repeaters

Age

11 to 14

Challenge level

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
problem
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
Latin numbers

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

Explore a number pattern which has the same symmetries in different bases.
problem
Binary squares

Age

16 to 18

Challenge level

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?