Question

Draw the linear arrangement: "A child must play five games--P, Q, R, S, and T--one after another, not necessarily in that order. The games must be played according to the following conditions:

The child plays exactly two games between playing S and playing T, whether or not S is played before T.
P is played immediately before Q is played.

Answer 1

The question involves arranging games P, Q, R, S, and T in a linear order following specific rules. Two games must be played between S and T and P must be played immediately before Q. Possible arrangements include RPQS or TSPQR among others, ensuring the conditions are met.

Step-by-step explanation:

The student is asking about arranging five games (labeled P, Q, R, S, and T) into a linear order based on given conditions:

• There must be exactly two games played between S and T.
• P is played immediately before Q is played.

To visualize this, we can consider the following scenarios:

1. If S is played before T: S, game1, game2, T
2. If T is played before S: T, game1, game2, S

Since P must be played immediately before Q, they form a pair (PQ).

Considering these conditions, one possible arrangement could be:

• First scenario (S before T): RPQS (remaining game R at start)
• Second scenario (T before S): TSPQR (remaining game R at the end)

There can be other arrangements as well based on the sequence of S and T, and where P and Q are placed, but all must satisfy the given conditions.