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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}.

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Common Divisor

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

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Hypotenuse Lattice Points

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

Different by One

Age 14 to 16 Challenge Level:
Be systematic : start with red rods and try light green, then purple, and so on, working through the rods in order of size.

Next have light green with purple, then yellow, and so on.

Next take purple . . . you get the idea?

Make careful notes - also a table might be good.