Logic Puzzles
“Uncle Bob”

Each month in 2020 I plan to feature a different type of logic puzzle. This month it’s…

Some details will seem to be missing from the following teasers. But NO. The needed info is all there. What is needed is, in Hercule Poirot’s terms, “the exercising of the little gray cells.”

1. Train Tunnel. [An oldie, but a goodie.] Two children, Freda and Max entered an express train tunnel. They knew they shouldn’t. They were unaware that they were two-fifths of the way through when they heard the train whistle. In a panic they ran – in opposite directions – at 15 miles per hour. By a split second each, both escaped being killed. How fast was the train going?

2. The Hiker.. A hiker set out at 8 a.m. climbing a mountain at the rate of one-and-a-half miles per hour. He then spent 12 hours camping at the top. After that stay he went down the same trail at four-and-one-half miles per hour, reaching the bottom at noon the next day. How long was the trail?

3. Book Price. A book costs \$10.00 plus half of its price. What does it cost?

4. Clock Bears Watching. A clock repairman, being ill, sent his apprentice on a house call to fix a 12-hour wall clock. The apprentice was quite thorough, even removing the clock hands to keep them safe during the process which turned out to be extensive. He finished the job well after sundown. Eager to get home, our man quickly replaced the clock hands to match his watch which read 6 p.m.

The apprentice reached home but in a short while got a call from the customer saying that the clock showed the wrong time. Our man returned to the home, showed the owner his watch and the clock which both read the correct time, and he returned home, shaking his head.

Early the next morning, the owner called again complaining that the clock was behaving nuttily. The apprentice made yet another visit, and … the clock and watch both read the same correct time. Both men were honest. What was going on?

5. Party Shakes. A party was attended by ten people: the hosts Mr. and Mrs. Smith and four other couples. During the course of the evening some, bit not all, pairs of people shook hands. No one shook hands with the same person twice, and no couples shook hands with one another. Both hosts shook some hands. At party’s end Mrs. Smith asked each person (other than herself) how many hands they shook. They all reported accurately a different number.

How many hands did Mr. Smith shake? Note well that one host took the poll, but we ask about the other host.

6. Crowded Field. Reported in the Athens Times: In yesterday’s mile run, Danny placed exactly in the middle of all finishers. Kevin placed lower – in eleventh place, and Kurt finished eighteenth. How many were in the race and where did Danny place?

Sources:
Richard Guy, et.al. The Inquisitive Problem Solver
Steven Krantz, Techniques of Problem Solving
Boris Kordemsky, The Moscow Puzzle Book
Raymond Smullyan, The Riddle of Scheherazade

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