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Sunday Afternoon Maths LVIII

Posted on 2017-01-01

Factorial pattern

$$1\times1!=2!-1$$ $$1\times1!+2\times2!=3!-1$$ $$1\times1!+2\times2!+3\times3!=4!-1$$
Does this pattern continue?

Placing plates

Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?
If you enjoyed these puzzles, check out Sunday Afternoon Maths LXVI,
puzzles about parabolas, or a random puzzle.