12 cards of three kinds in a row
Source: VI May Olympiad (Olimpiada de Mayo) 2000 L1 P5
September 22, 2022
combinatorics
Problem Statement
In a row there are cards that can be of three kinds: with both white faces, with both black faces or with one white face and the other black. Initially there are cards with the black side facing up. The first six cards from the left are turned over, leaving cards with the black face up. The six cards on the left are then turned over, leaving cards with the black face up. Finally, six cards are turned over: the first three on the left and the last three on the right, leaving cards with the black face up. Decide if with this information it is possible to know with certainty how many cards of each kind are in the row