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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}.


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.

Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

2-digit Square

Age 14 to 16
Challenge Level

2-digit Square printable sheet

A $2$-digit number is squared. When the $2$-digit number is reversed and squared, the difference between the squares is also a square.


What is the $2$-digit number?