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

2019 Hong Kong TST, 5
Tags: hong kong , combinatorics , combinatorial geometry
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?

2006 Hong Kong TST., 2
Tags: hong kong , functional equation , function
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)