458: HAPPY THANKSGIVING
Grandmother Brown is going to host a huge family gathering on Thanksgiving Day. She has eight grandchildren, and this year she has decided that they will all help with serving or cleaning up. The kitchen is small, so she must select four of the children to wash dishes after the meal. The others will help with serving during the meal.
The selection is not an easy matter, however, for there are jealousies and attachments among the children that prevent a free choice of four dishwashers. Can you help Grandmother select a dishwashing crew of four while satisfying all these whims?
- Travis will work with anybody.
- Michael won’t wash dishes unless Vinolia helps too.
- Vinolia won’t work with Jen.
- Nicholas won’t work without Funmi.
- Jen will work with anybody.
- Clark won’t wash dishes with Nicholas unless Stephen helps too, and won’t work with Vinolia unless Nicholas also helps.
- Stephen won’t work with both Michael and Vinolia, and won’t wash dishes with either Travis or Jen.
- Funmi won’t help unless either Michael or Clark wash dishes, and won’t work with Vinolia unless Stephen works too, and won’t work with both Travis and Jen.
Please state the names of the four grandchildren who will be washing the dishes, and give a full explanation of how you made your selection.
2780: THANKSGIVING TRAVEL
Zach is planning to drive to his parents’ house in Philadelphia for Thanksgiving. He lives in Pittsburgh so he can either take Route 30, which is a scenic drive, or take the Pennsylvania Turnpike. He’s trying to decide between the two routes. Here are the details that he’s considering:
– distance is 305 miles each way
– toll road charge is $9.00 each way
– 1/61 of the trip is city driving and 60/61 is highway driving
– distance is 372 miles each way
– no tolls
– 1/3 of the trip is city driving and 2/3 is highway driving
Gas costs on the average $1.60 per gallon. Zach’s car gets 25 miles per gallon in the city and 30 miles per gallon on the highway. (Route 30 involves more city driving because he’d be driving through a lot of small towns.)
Explain which plan is the most economical (not considering the time involved or the wear and tear on his car).