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Rational Round
Age 16 to 18
Challenge Level 
Why do this problem?
It provides an easy starter where all students ought to have success. It may seem surprising that some circles contain points with rational coordinates and others do not. The second half can be proved using modulus arithmetic and an argument by contradiction.Key Question
What if the circle$x^2 + y^2 = 3$ DID contain rational points...?Possible support
The article Modulus Arithmetic and a Solution to Dirisibly Yours gives a beginnersintroduction to modulus arithmetic and it is a good idea to try the problem Dirisibly Yours first.You may also like
Old Nuts
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?
