4
Part of 2017 Tuymaada Olympiad
Problems(2)
Geometry or number theory
Source: Tuymaada 2017 Junior Level
7/17/2017
A right triangle has all its sides rational numbers and the area . Prove that there exists a right triangle, different from the original one, such that all its sides are rational numbers and its area is .Tuymaada 2017 Q4 Juniors
number theory
Tuymaada 2017 P4 Day 1 Senior League
Source:
7/25/2017
There are 25 masks of different colours. k sages play the following game. They are shown all the masks. Then the sages agree on their strategy. After that the masks are put on them so that each sage sees the masks on the others but can not see who wears each mask and does not see his own mask. No communication is allowed. Then each of them simultaneously names one colour trying to guess the colour of his mask. Find the minimum k for which the sages can agree so that at least one of them surely guesses the colour of his mask.
( S. Berlov )
combinatorics