Talk:Analytic Maths for Olympiads
Part of the School of Olympiads
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A picking game (problem on induction)
There is a heap of matches. 2 players take turns to pick 1 or 2 matches. The winner is the person who picks the last match.
- Who wins for 5 matches (if no player misses a chance to win or draw)?
- Is there a general strategy for any number of matches (to force a win or a tie for either side)?
- What is the strategy if existing?
A Rootful Question
Prove the following:
A problem on functions
Find all pairs of real numbers (a,b) such that: f(x)= x2 + ax + b If q is a root of f(x) then q2-2 is also a root