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Pythagoras Mod 5
Age 16 to 18
Challenge Level 
Prove that for every right angled triangle which has sides with integer lengths:
- the area of the triangle is even and
- the length of one of the sides is divisible by 5.
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In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?
