This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2006 Hong Kong TST., 2
The function $f(x,y)$, defined on the set of all non-negative integers, satisfies (i) $f(0,y)=y+1$ (ii) $f(x+1,0)=f(x,1)$ (iii) $f(x+1,y+1)=f(x,f(x+1,y))$ Find f(3,2005), f(4,2005)
function hong kong functional equation algebra functional equations

2019 Hong Kong TST, 5
Is it is possible to choose 24 distinct points in the space such that no three of them lie on the same line and choose 2019 distinct planes in a way that each plane passes through at least 3 of the chosen points and each triple belongs to one of the chosen planes?
hong kong combinatorics combinatorial geometry double counting modular arithmetic