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Really Mr. Bond
Age 14 to 16
Challenge Level 
Is it always the case that when you square a number whose last digit is 5 you always end with 25?
By breaking the number down into a form (x + 5) it may then be possible to see what is happening and why.
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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}.
Novemberish
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.
