Jim Propp’s “Swine in a line” game part 2

Last week I saw a really fun new question from Jim Propp:

If there are pigs in pens 2, 7, and 9, what's the unique winning move? Be the first to find the answer! https://t.co/nlj8X6307f

— James Propp (@JimPropp) June 14, 2017

Here’s the first project that we did on the game:

Jim Propp’s Swine in a Line game

Today we returned to the game to see if we could make any more progress understanding how it worked.

First we reviewed the rules and decided on an initial approach to studying the game for today:

Their first idea was to try to keep the two ends open since they knew the result when you reached the position with only 1 and 9 open.

Now we tried to study a bit more. The kids were having trouble seeing a path forward, so I just let them play.

At the end of the last video we were studying a position with all of the pens filled except for 7 and 9. In this video we searched for a winning move.

Finally, we took one more crack at solving the game. They boys got very close to the main idea, about an inch away(!), but didn’t quite get over the line.

The boys were really interested in the game and we kept talking for about 30 min after the end of the project. During that talk they did uncover the main idea. After that we played several games where they followed the strategy and they were able win against me every time following that strategy. It was a fun way to end the morning.