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.
- At what time will the two hands coincide?
- At what time will the two hands first stand at right angles to each other?
- 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
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
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
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
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