No Slippage

Probability Level 3

When we place 1×21 \times 2 dominoes on a board that isn't completely covered, sometimes we are able to move a domino horizontally or vertically. For example, in this 3×2 3 \times 2 board, the yellow domino can move horizontally while the blue domino is stuck.

Consider an 8×8 8 \times 8 board tiled with several 1×2 1 \times 2 dominos. What is the minimum number of dominos for which there exists an arrangement in which no domino can move (horizontally or vertically) into another position?

Details and Assumptions:

  • The dominos are not allowed to stick out of the board or overlap.
  • We get to choose the placement of the dominos.

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