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Problems(2)
Determination of the color of the ball
Source: IV Caucasus Mathematic Olympiad
4/7/2019
In the kindergarten there is a big box with balls of three colors: red, blue and green, 100 balls in total. Once Pasha took out of the box 30 red, 10 blue, and 20 green balls and played with them. Then he lost five balls and returned the others back into the box. The next day, Sasha took out of the box 8 red, 18 blue, and 48 green balls. Is it possible to determine the color of at least one lost ball?
combinatorics
Paint the largest number in each square
Source: IV Caucasus Mathematic Olympiad
4/7/2019
Pasha placed numbers from 1 to 100 in the cells of the square , each number exactly once. After that, Dima considered all sorts of squares, with the sides going along the grid lines, consisting of more than one cell, and painted in green the largest number in each such square (one number could be colored many times). Is it possible that all two-digit numbers are painted green?
combinatorics