Place value

problem
X marks the spot

Age

11 to 14

Challenge level

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
problem
Back to basics

Age

14 to 16

Challenge level

Find b where 3723(base 10) = 123(base b).
problem
Just repeat

Age

11 to 14

Challenge level

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?
problem
Three times seven

Age

11 to 14

Challenge level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
problem
Phew I'm factored

Age

14 to 16

Challenge level

Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
problem
What an odd fact(or)

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
list
Ten-ness of ten

Age

5 to 7

These tasks will help children understand the 'ten-ness' of ten, a fundamental part of place value.
problem
Writing digits

Age

5 to 7

Challenge level

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?
problem
Two-digit targets

Age

5 to 7

Challenge level

You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?