LSAT 21, Game 2 Setup, Colored Light Bulbs, LSATHacks

Game Setup

This is a type of pattern game:  it’s fairly rare. There are only three spots to place light bulbs and there are nine light bulbs total. There are three light bulbs of each color.  It is possible in theory to have all bulbs be the same color (though the rules will limit this).

The first step should be to draw our three rules.

These three diagrams show the three separate rules. I’ve drawn the sufficient condition in a box, and placed the necessary condition on the diagram.

Rule 1: P is in leads to Y in 2. Rule 2: G in 2 leads to G in 1. Rule 3: P or Y in 3 leads to P in 2.

To be clear:  the three lines are three separate scenarios.

Next, we have to see if we can combine any of these rules. Look at the first one; P is in slot 1 and Y is in slot 2. What can we put in slot 3?

Well, The third rule tells us that if P or Y is in 3, then P is in 2. So we can’t put P or Y in 3 in the first rule. We have to put G there.

The third rule also lets us make the same deduction about the second rule. If G in 1 and in 2 then 3 must also be G. Why?  If P or Y were in 3 then 2 would have to be P, not G.

The only restriction in the third rule is that spot 1 can’t be P. That would make 2 yellow, not P. So the first slot is Y or G in the third scenario.

Here’s what that looks like. Remember, these three diagrams show what happens when the first, second and third rules apply:

You can also draw what the diagram would look like if no rules were triggered. This doesn’t end up being useful, but it may help to understand the game.

In the third spot, only G doesn’t trigger a rule. In the second spot P and Y don’t trigger rules. And in the first spot Y and G don’t trigger rules.

So placing any of these variables in these spots causes nothing to happen. Anything else causes one of the three rules above to come into play.

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