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# Pegity - white to win

## Question

OK so I was a kid once, back in the 40s and 50s, and we had this game called Pegity.

It had a board with a 16x16 array of holes, and in turn each of 2-4 players inserted a peg of his own color into a hole. The object was to get 5 pegs of your color in a row: vertically, horizontally or diagonally. Not every game was won: similar to tic-tac-toe, you could run out of holes. But with only two players, there was usually a win.

For simplicity let's shrink to a 9x9 board, mark the holes like in chess (A1, E7, etc.) and say that after O and X have each made three moves we have this position, with O to move:

1  2  3  4  5  6  7  8  9
A  +  +  +  +  +  +  +  +  +
B  +  +  +  +  +  +  +  +  +
C  +  +  +  +  +  +  +  +  +
D  +  +  +  +  +  +  +  +  +
E  +  +  +  +  O  +  +  +  +
F  +  +  +  O  +  O  +  +  +
G  +  +  +  +  X  +  +  +  +
H  +  +  +  X  +  X  +  +  +
I  +  +  +  +  +  +  +  +  +

With best play by both players, how soon can O win?
Use chess notation (naming the holes, in two columns) to list the moves.

## Recommended Posts

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Is O win if we get XOOOOOX?

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7 hours ago, aiemdao said:

Is O win if we get XOOOOOX?

Yes. That’s a win for white

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I think after 7 move

( O-X ) : E4 -H5 , H3-H7 , H8-D4, E6-E2, D6-G7, C6-B6, G6

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12 hours ago, aiemdao said:

I think after 7 move

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( O-X ) : E4 -H5 , H3-H7 , H8-D4, E6-E2, D6-G7, C6-B6, G6

Spoiler

I think X could play better ( his move 4 or move 5 ) to extend the game past 7 moves.

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It takes 8 moves.  All of the second player's moves are forced, but he usually has two ways to respond.  In either case, though, the second player can't prolong the game any longer than move 8 (that I can find).

1. f6, f3
2. d6, g3
3. d4, g7
4. e4, g4
5. g6, d3
6. e6, c6
7. e3, resigns

One of 8. e2 and 8. e7 is unstoppable.

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7 hours ago, Molly Mae said:

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It takes 8 moves.  All of the second player's moves are forced, but he usually has two ways to respond.  In either case, though, the second player can't prolong the game any longer than move 8 (that I can find).

1. f6, f3
2. d6, g3
3. d4, g7
4. e4, g4
5. g6, d3
6. e6, c6
7. e3, resigns

One of 8. e2 and 8. e7 is unstoppable.

Spoiler

4 in a row with one end unblocked, or 3 in a row with both ends unblocked, force the next move. A forced win must do this on each move. Nice.

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