Place value

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
DOTS division

Age

14 to 16

Challenge level

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
problem
BT... eat your heart out

Age

16 to 18

Challenge level

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?
problem
Purr-fection

Age

16 to 18

Challenge level

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

Age

7 to 11

Challenge level

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
problem
Number detective

Age

5 to 11

Challenge level

Follow the clues to find the mystery number.
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
6 beads

Age

5 to 7

Challenge level

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
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?
article
A story about absolutely nothing

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.