The local community theater is staging 4 plays consecutively over 22 days. One is a farce, one a musical, one a mystery, and one a hystorical drama. One of them will run for 3 weeks, another 5 weeks, another 6 weeks, and another 8 weeks, not necessarily in that order.
- The musical will not be running in week 15.
- The play running in week 13 will have closed before week 17.
- The historical drama will be running during week 14.
- In week 10 the farce will be running.
- The mystery will run before the musical, and will run for longer than the historical drama but shorter than the farce.
What is the sequence of the plays' runs, and how many weeks will each run?
From Readers Digest, March/April 2025.
The farce is followed by the historical, they are either consecutive or have the three-week play in between.
Assume there is the three-week play in between, then the farce ends on week 10, but there is no combination of plays that makes up 10 weeks. So then the assumption is false and farce must be immediately followed by the historical.
The mystery precedes the musical. If they are not consecutive then those two plays are at either end of the farce/historical block.
The farce running in week 10 has either one or two plays scheduled before it. If two plays precede the farce then they must be the mystery then the musical. Assume this is the case. Then one of the mystery or musical runs for three weeks and the other is five or six weeks.
Either way the farce must run at least five weeks. If the mystery and musical are 3 and 5 weeks then the farce starts on the 9th and runs at least to the 15th, contradicting clue 2; similarly of the mystery and musical are 3 and 6 weeks then the farce starts on the 10th and runs at least to the 15th, again contradicting clue 2. So the assumption is false and only one play can precede the farce.
At this point it is known that the plays are in order: Mystery, Farce, Historical, Musical.
The mystery runs 5 or 6 weeks, the farce runs 6 or 8 weeks, and the historical runs 3 or 5 weeks. The musical cannot be 8 weeks from clue 1. Then the farce runs 8 weeks.
The farce ends on or before week 13. Since it runs 8 weeks then the mystery can run at most 5 weeks. Then the mystery must be exactly 5 weeks. This leaves 3 weeks for the historical and finally 6 weeks for the musical.
The theatre schedule is weeks 1-5 are the mystery, weeks 6-13 are the farce, weeks 14-16 are the historical, and weeks 17-22 are the musical.
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