Which one of the following could be an accurate list of the contestants who play in each of the four games?

Gabby on March 31 at 01:15AM

Where's N/P in the first scenario?

In the set-up, how come Nam and Pachai aren't accounted for in the first scenario?

1 Reply

Skylar on March 31 at 04:21AM

@Gabby_teixeira, happy to help.

The second scenario we derived during our set-up is more restrictive than the first scenario we derived. We do not mention N or P in the first scenario because our scenario is too open to determine where these variables could go, unlike the more limited second scenario.

Scenario 1: _S _O _S _ _
1 2 3 4
Scenario 2: _ _ _S _O _S
1 2 3 4

Rule #2 tells us that L must be placed in the last game. We can place L in Game 4 in Scenario 1 and still have an open spot in that game. However, we already have S in Game 4 in Scenario 2, so placing L in the other spot closes that game.

Rule #1 tells us that T cannot play in the first or third games. This only leaves the second or fourth games as options for T. The fourth game in Scenario 2 is full, so T must be placed in the second game there. However, the fourth game still has an open spot in Scenario 1, so T has options there. Drawing out these options is unnecessary, so we do not mark T, leaving it open.

Rule #3 tells us that N does not go in the same game as P. Scenario 2 only has two different games open, so we can split N and P up accordingly. Since Scenario 1 could have room in any of the games, we do not mark N and P.

Does that make sense? Please let us know if you have any other questions and best of luck with your studies!