Rock, Paper, Scissors (part 2)

by admin on April 7, 2013

A month ago I wrote a post called Rock, Paper, Scissors, where I posed the following problem: Can you come up with three half-positions (that is, positions for one player only, written in English Descriptive Notation), called “Rock,” “Paper,” and “Scissors,” such that:

a) When the pieces are set up with White playing Rock and Black playing Scissors, White wins even if it’s Black to move;

b) When the pieces are set up with White playing Scissors and Black playing Paper, White wins even if it’s Black to move;

c) When the pieces are set up with White playing Paper and Black playing Rock, White wins even if it’s Black to move.

As you can see in the original post, I came up with a solution in which each half-position has only three pieces.

Well, that record didn’t last for long. A few days later I got an e-mail from none other than GM Sam Shankland, who found the best possible solution (meaning the one with the least possible material). In his Rock, Paper, Scissors positions, each half-position has only a king and a pawn. You can’t top that!

Curiously, there was a mistake in his original solution, which may have been due to overlooking the condition that the given side is supposed to win even if it’s the other player’s move. In his version, one of the positions was drawn under that condition. However, it was very easy to fix the mistake so that it really is a Rock-Paper-Scissors solution, and in fact I think the fix made the solution slightly more aesthetically pleasing.

However, I’m not going to show you the flawed version. Here is the corrected version, with full credit to Sam because he had the right idea.

Rock = K on KR2, P on KN5

Paper = K on KR2, P on QN4

Scissors = K on QN6, P on QN4.

Rock vs. Scissors:

Black to move, White wins

Black’s king is in the worst possible place: in the way of his own pawn, and also too far from White’s pawn to stop it. In the resulting pawn race, White will queen his pawn and Black will only get his pawn to b2. Because it is a knight pawn, not a rook pawn or bishop pawn, Black loses.

Paper vs. Rock:

Black to move, White wins

This one is pretty easy to analyze. Once again, Black’s king is outside the square of White’s pawn and cannot get inside the square in one move. Also, the “Reti trick,” where you fake toward the queenside and come back to the kingside (e.g. … Kh7-g6-f5-f4) will not work here because White’s king easily has good enough defensive position.

Scissors vs. Paper:

Black to play, White wins.

This is the easiest position of all. Black on move can do nothing about the fact that White is going to take on b5 and march his b-pawn.

An ingenious solution! I think this just about puts the Rock-Paper-Scissors problem to bed. (By the way, I would have posted Sam’s solution earlier, but a little event called the Candidates Tournament took precedence.)

In other news, I am departing in two days for a mixed business and family trip. I’m going to Virginia to give a talk at Emory and Henry College, and then to Tennessee to visit my father, who just had his 80th birthday. I’m hoping that the last part of the trip will give me some nice leisure time for chess study, but I don’t know whether there will be time to write any blog posts. We’ll see.

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{ 1 comment… read it below or add one }

Tadek April 9, 2013 at 6:23 am

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