MathDB

4

Part of 2005 Peru MO (ONEM)

Problems(1)

same no of chips on each sqaure of 5x5 board, after many moves

Source: 2005 Peru MO (ONEM) L3 p4 - finals

11/23/2022
On the grid board shown, a token is placed on each white space. https://cdn.artofproblemsolving.com/attachments/3/2/0060b2436edb0ce25160d2f94f379defef237c.png A move consists of choosing four squares on the board that form a "TT" in any of the shapes shown below, and add a token to each of these four squares. https://cdn.artofproblemsolving.com/attachments/8/c/3890aed5289ec9ea2d147f8000a0422c233029.png Is it possible, after carrying out several moves, to get the 2525 squares to have the same amount of chips?
combinatorics