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Adding All Nine

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

N000ughty Thoughts

How many noughts are at the end of these giant numbers?

DOTS Division

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}.

Robotic Rotations

Age 11 to 16
Challenge Level

It might be a good idea to start by working out the rotational symmetry of each image...

For example, this picture has rotational symmetry of order 4. That means there are four copies in a full $360^{\circ}$ turn. So each rotation must be...