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Hi all, I've been scouring the forums/internet for an explanation to this game but to no avail. I had an extremely hard time figuring out the major deduction (assuming there was indeed one) and ended up spending 15+ mins on this one particular game, working through each answer choice it feels like. I even had to save the last two "must be true" questions for last.

The only major thing I was able to infer was that out of the Topazes, there could be anywhere from 2-3 selected and I represented this by w/z __ (__). What else was I missing here?

That's a great inference. It tells us that we can only have either 2 or 3 Topazes, which greatly restricts the number of variables that can be selected from each group.

If we have only 2 topazes, then we will have either 1 ruby and 3 sapphires, or 3 rubies and one sapphire.

If we have 3 topazes, we will have either 3 rubies and 0 sapphires, 0 rubies and 3 sapphires, 1 ruby and 2 sapphires, or 2 rubies and 1 sapphire.

More succinctly, for rubies, sapphires, and topazes, respectively:

R-S-T
1-3-2
3-1-2
3-0-3
0-3-3
1-2-3
2-1-3

This is the key inference for the game and should make the questions much easier.

Thanks LSAT Blog. When I ran through the different possibilities, I assumed that there were simply too many for them to be useful (I'm used to numerical distributions simplifying a game into 2-3 possibilities), but now I can see how listing them would have definitely helped me finish in a more timely fashion. I'm glad to hear I wasn't blindsided by a huge inference.

Big fan of your blog and your contributions. Keep up the great work!

LSAT Blog wrote: R-S-T
1-3-2
3-1-2
3-0-3
0-3-3
1-2-3
2-1-3

This is the key inference for the game and should make the questions much easier.

I got that there would be either 2-3 topazes, but didn't even think to make this diagram. Did you just make that when you were diagramming the other rules? I also took just over 15 min and spent way too long on 14, which your diagram solves immediately.

spets wrote:Thanks LSAT Blog. When I ran through the different possibilities, I assumed that there were simply too many for them to be useful (I'm used to numerical distributions simplifying a game into 2-3 possibilities), but now I can see how listing them would have definitely helped me finish in a more timely fashion. I'm glad to hear I wasn't blindsided by a huge inference.

Big fan of your blog and your contributions. Keep up the great work!

Glad to help, spets!

2011Law wrote:I got that there would be either 2-3 topazes, but didn't even think to make this diagram. Did you just make that when you were diagramming the other rules? I also took just over 15 min and spent way too long on 14, which your diagram solves immediately.

I'd create it after laying out the other rules. One indication that distribution plays a role in this game is that many questions/choices refer to the categories of variables (R, S, T), rather than the variables themselves (the specific stones).