Will they fit? – 3
I have a Puzzle consisting of pieces.
What is the minimum number of pieces I have to draw randomly from a pile to be guaranteed that there is at least one square (in the solved puzzle) whose pieces all have been drawn?
Details and Assumptions:
- Every piece is equally likely to be picked. I don't look whether the first piece has a straight edge or similar tricks.
- Every piece only fits together with its neighboring pieces, and there is a unique solution to the puzzle.
- Two pieces that only share a corner are not joined
- All 100 pieces of the puzzle are in the pile, but no other pieces
The answer is 92.
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1 solution
91 is not enough: if all the nine 3i-3j pieces are missing (labeling the pieces like the entries of a matrix), then each 3 × 3 square will miss exactly one piece. But 92 suffices: Consider nine disjoint 3 × 3 squares; at least one of them will be complete.