Place value

problem

Seven Up

Age

11 to 14

Challenge level

3 out of 3

The number 27 is special because it is three times the sum of its digits 27 = 3 (2 + 7). Find some two digit numbers that are SEVEN times the sum of their digits (seven-up numbers)?
problem

Quick Times

Age

11 to 14

Challenge level

3 out of 3

Can you verify and generalise these equations?
problem

Basically

Age

11 to 14

Challenge level

3 out of 3

The number 3723 (in base 10) is written as 123 in another base. What is that base?
problem

Please Explain

Age

11 to 14

Challenge level

3 out of 3

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.
problem

Back to the Planet of Vuvv

Age

11 to 14

Challenge level

3 out of 3

There are two forms of counting on Vuvv - Zias count in base 3 and Zepts count in base 7. Can you work out in which direction the Zias and Zepts were looking, based on the information you're given?
problem

Six Times Five

Age

11 to 14

Challenge level

3 out of 3

How many six digit numbers are there which DO NOT contain a 5?
problem

What an Odd Fact(or)

Age

11 to 14

Challenge level

3 out of 3

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
problem

Skeleton

Age

11 to 14

Challenge level

3 out of 3

Can you reconstruct the long division calculation from the 'skeleton'?
problem

Big Powers

Age

11 to 16

Challenge level

3 out of 3

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

eNRICHing Experience

Age

14 to 16

Challenge level

1 out of 3

Find the five distinct digits N, R, I, C and H in the following nomogram