LG Problem Set #2: December 2005 Qs 18-22

[smile22]

Hello,

I am having difficulty with the December 2005 LG game that appears in the LG Problem Set Package. It is question #23 in the packet, and is referring to three folk groups and two rock groups that perform on a north or south stage. My biggest problem is in the set up and how to initially approach this game. Could you please help? Thank you very much.

[Jason Schultz]

Hi smile22 (good attitude!)

This game is best approached as an advanced linear setup. I chose to create a diagram with 2 rows(one for each stage) and 4 columns (one for each time slot). So for me it looked like this, sorry about the formatting:

6 8 10 12
N ____ _____ _____ __X___
S _X_ _____ _____ _____

Also from the scenario, you know that there's no performance on the North stage at 12, nor the South one at 6. I used that rule to block those with Xs.

So then you have the six bands, subdivided by genre: G, H, L are folk bands, P, Q, T are rock groups.

Rule 1) This is an easy split rule. P only has two possibilities so immediately discard an answer that has P anywhere else.

Rule 2) G>H, very simple. Note that the two stages are playing at the same time so G and H can never appear in the same column.

Rule 3) The inference of this rule is that the 10 slots are either both folk, or both rock. In the latter case, P is accounted for on the ends, so the 8 slots are both folk.

Rule 4) L & T can never be in the same row.

Rule 5) Q has to be after a folk group, which means Q cannot be first. If Q is at 12, P is as 6. If Q is at 8, a folk group is at 6 and P is at 12.

See if that setup helps.

[smile22]

Thank you for the feedback. This was very helpful. In my initial set up I didn't "block out" slot 6 for the South side and slot 12 for the North side. X'ing out those slots definitely makes a difference and makes things easier to visualize. Also, for some reason, I didn't truly conceptualize the third rule, which prevented me from making key inferences.

Thank you for your help and for the timely response!