# Locating the Loot

This is a straight-forward problem from Geoffrey Mott-Smith in 1954.

“A brown Terraplane car whizzed past the State Police booth, going 80 miles per hour. The trooper on duty phoned an alert to other stations on the road, then set out on his motorcycle in pursuit. He had gone only a short distance when the brown Terraplane hurtled past him, go­ing in the opposite direction. The car was later caught by a road block, and its occupants proved to be a gang of thieves who had just robbed a jewelry store.

Witnesses testified that the thieves had put their plunder in the car when they fled the scene of the crime. But it was no longer in the car when it was caught. Reports on the wild ride showed that the only time the car could have stopped was in doubling back past the State Police booth.

The trooper reported that the point at which the car passed him on its return was just 2 miles from his booth, and that it reached him just 7 minutes after it had first passed his booth. On both occasions it was apparently making its top speed of 80 miles per hour.

The investigators assumed that the car had made a stop and turned around while some members of the gang cached the loot by the roadside, or perhaps at the office of a “fence.” In an effort to locate the cache, they assumed that the car had maintained a uniform speed, and allowed 2 minutes as the probable loss of time in bringing the car to a halt, turning it, and regaining full speed.

On this assumption, what was the farthest point from the booth that would have to be covered by the search for the loot?”

See Locating the Loot for solutions.

# After Five O’clock

This is a fairly extensive clock problem by Geoffrey Mott-Smith from 1954.

“The clock shown in the illustration has just struck five. A number of things are going to happen in this next hour, and I am curious to know the exact times.

1. At what time will the two hands coincide?
2. At what time will the two hands first stand at right angles to each other?
3. At one point the hands will stand at an angle of 30 degrees, the minute hand being before the hour hand. Then the former will pass the latter and presently make an angle of 60 degrees on the other side. How much time will elapse between these two events?”

See After Five O’Clock for solutions.

# Handicap Racing

This is a nice variation on a racing problem by Geoffrey Mott-Smith from 1954.

“On one side of the playground some of the children were holding foot-races, under a supervisor who handicapped each child according to age and size. In one race, she placed the big boy at the starting line, the little boy a few paces in front of the line, and she gave the little girl twice as much headstart over the little boy as he had over the big boy. The big boy won the race nevertheless. He overtook the little boy in 6 seconds, and the little girl 4 seconds later.

Assuming that all three runners maintained a uniform speed, how long did it take the little boy to overtake the little girl?”

See the Handicap Racing for solution.

# Refabulating Widgets

This is a work problem from Geoffrey Mott-Smith from 1954.

“ ‘If a man can do a job in one day, how long will it take two men to do the job?’

No book of puzzles, I take it, is complete without such a question. I will not blame the reader in the least if he hastily turns the page, for I, too, was annoyed by “If a man” conundrums in my schooldays. Besides, the answer in the back of the book was always wrong. Everybody knows it will take the two men two days to do the job, because they will talk about women and the weather, they will argue about how the job is to be done, they will negotiate as to which is to do it. In schoolbooks the masons and bricklayers are not men, they are robots.

Strictly on the understanding that I am really talking about robots, I will put it to you:

If a tinker and his helper can refabulate a widget in 2 days, and if the tinker working with the apprentice instead would take 3 days, while the helper and the apprentice would take 6 days to do the job, how long would it take each working alone to refabulate the widget?”

See Refabulating Widgets for a solution.

# Alcan Highway Problem

This work problem from Geoffrey Mott-Smith is a little bit tricky.

“An engineer working on the Alcan Highway was heard to say, “At the time I said I could finish this section in a week, I expected to get two more bulldozers for the job. If they had left me what machines I had, I’d have been only a day behind schedule. As it is, they’ve taken away all my machines but one, and I’ll be weeks behind schedule!”

How many weeks?”

See the Alcan Highway Problem for a solution.

# An Intercept Problem

This is a straight-forward problem by Geoffrey Mott-Smith from 1954.

“Three tangent circles of equal radius r are drawn, all centers being on the line OE. From O, the outer intersection of this axis with the left-hand circle, line OD is drawn tangent to the right-hand circle. What is the length, in terms of r, of AB, the segment of this tangent which forms a chord in the middle circle?”

See An Intercept Problem for solutions.