Setup and Rule Diagrams

[LawSchoolDream]

Setup

pt80 game 3 setup-2.jpg


Please post below with any questions!

I'm curious. When you diagrammed this, does a left \ indicate NEVER and / indicate both directions?

[Adam Tyson]

Nope, nothing special about the direction of the slash. A slashed out block just means "this can't happen."

[npant120]

Is there a faster way to arrive at the inference that Hw must be with Io in the 4th wall? I just tried to put Go and Ho there and realized neither worked, but I'm not sure if there was some inherent inference I could have made to find this out more quickly?

[Robert Carroll]

Nimisha,

There's not much that can be there. There are only 8 things in the game total. Now, that doesn't mean I'm going to try all 8 things in all 8 spaces to brute-force inferences. But the upper position of wall 4 is particularly restricted. It can't be an oil at all, which cuts out 4 of the 8 options right away. It also can't be by Isaac (can't be Isaac on a wall twice) or Franz (third rule). So it's a watercolor by G or H. The G watercolor is spoken for by the 4th rule.

Robert Carroll

[npant120]

Nimisha,

There's not much that can be there. There are only 8 things in the game total. Now, that doesn't mean I'm going to try all 8 things in all 8 spaces to brute-force inferences. But the upper position of wall 4 is particularly restricted. It can't be an oil at all, which cuts out 4 of the 8 options right away. It also can't be by Isaac (can't be Isaac on a wall twice) or Franz (third rule). So it's a watercolor by G or H. The G watercolor is spoken for by the 4th rule.

Robert Carroll

Hi Robert,

Thank you for your explanation. I did have a question regarding oil paintings - how do you know that the oil paintings cannot be grouped together on a wall?

[Robert Carroll]

Nimisha,

This is an inference from the first rule. If no wall can be W over W, then no wall can be O over O either. Assume a wall is O over O. Then the four remaining W are crammed into the remaining three walls. By the Pigeonhole Principle, at least one wall has W over W, violating the first rule. So the assumption that a wall is O over O leads to a contradiction.

Robert Carroll