# Varsity Math, Week 152

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Welcome to Varsity Math, the weekly math puzzle column by the National Museum of Mathematics and featured each weekend in the Wall Street Journal.

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### Nuts and Bolts

A customer at the hardware store has purchased a package of five nuts and one of eight bolts, each package priced separately. If the bill for the nuts and the bill for the bolts are multiplied or added, the result is \$7.20 either way.

What are the prices of nuts and bolts individually if neither item costs more than a dollar?

### Bridge Crossing

Six hikers must cross a bridge. A maximum of two people can cross at one time. It is night, and they need their one flashlight to guide them on any crossing. Each person walks at a different speed: Person 1 takes 1 minute to cross; Person 2 takes 3 minutes; Person 3 takes 4 minutes; Person 4 takes 6 minutes; Person 5 takes 8 minutes and Person 6 takes 9 minutes. A pair must walk together at the rate of the slower person’s pace. They all begin on the same side.

What is the least amount of time they need to get all six across the bridge?

## Solutions to week 151

To solve Three Burning Ropes, simultaneously light the first rope from one end and the second rope from both ends, reducing the first rope to 12 minutes remaining when the second rope is consumed. At that instant, burn the third rope from one end and the first rope from both ends, reducing the third rope to 122 minutes remaining when the first rope is consumed. Now, burn the third rope from both ends for a 61-minute interval. In Prime Perimeter, John has 7 and 17 on his forehead.