Solutions

Logic Puzzles: Information. PLEASE!!

1. Train Tunnel. HINT. Don’t worry about the train at first. Draw pictures of where the kids are at the three key moments. Answer at the bottom.

2. The Hiker. HINT. A person walking three times faster will cover the same distance in one-third the time. Apportion accordingly.

3. Book Price. $20.00

4. Clock Bears Watching. In the darkened room the apprentice mixed up the mounting of the hands, The long hand pointed correctly to 12 at 6 pm, but it was mounted on the hour drive gear. In about two hours and ten minutes after 6 p.m., the long hand had moved from the 12 to the 2. The short hand, having counted 130 minutes, made two revolutions from the 6 and ten minutes more to just past the 8 on the dial. So at about 8:10 the clock was correct.

At 7:05 the next morning, that is, 13 hours and 5 minutes past 6 p.m., the long hand made one revolution from 12 plus one hour to 1 on the dial. The short hand made 13 complete revolutions from the 6 plus 5 minutes to end at the 7. Both the clock and the watch read 7:05.

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5. Party Shakes. No one shook more than 8 hands, since no one shook their spouse’s hand. But nine people, all but Mrs. Smith, responded with different numbers, so those numbers were 0, 1, 2, …, 8. Let S stand for the Smith couple, and let A, B, C, and D represent the other couples. Who shook no hands t all. We are told both hosts shook some, so let’s say Mr. A shook no hands. Then the four other couples had at most 7 hands available – not their spouses, not Mrs. Smith, and not Mr. A. Who then shook 8 hands? It has to be Mrs. A.

Leaving the A’s and their extreme social postures, we ask who shook 7 hands. Let it be Mr. B. The couples C, D, and the Smiths are now known to have shaken at least two hands, those of Mr. B and Mrs. A. But someone shook just one hand, and that must be Mrs. B. Continuing this line of reasoning we arrive at pairs of numbers for the Couples A, B, C, and D, and those pairs are zero and 8, 1 and 7, 2 and 6, and 3 and 5. That leaves the number 4 which is the number of hands that Mr. Smith shook.

6. Crowded Field. If Danny finished in the middle of the pack, then there were an odd number of runners. Since Kurt finished eighteenth there must have been at least 19 runners; however, if the field were 21 or more contestants, Kevin’s eleventh place finish would put him in the middle or even higher than Danny. So there were exactly 19 runners and Danny finished tenth.

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Nothing in Common

# 1-16 in order are epoch, grail, notch, lager, point, larch, inept, carol, thing, place, right, plane, choir, plant, chore, align.

Other solutions possible. Send us yours!

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Department of Words

Ferriswords

From left to right find PIRATE.

From right to left find SECRET.

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Five and Ten

Puzzle 1. Triumphant   Puzzle 2. Upholstery

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Fit for Four

1. slip  2. life   3. going    4. market

5. coal   6. pay    7. football    8. piece

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Crisscross Crunch

Across, in row order: casaba, abate, tenor; cola, lamina, naked; lemon, Monday, Yule; voter, terra, rancid; gene, newsy, Yemen.

Down, in column order: favor, Oregon, goner; canal, alone, never; Magi, girder, rose; pecan, any, Yankee; Doc, cello, loiter.

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Minicryprtic

Across 1. Spheres (pHs + sere)    4. Level (palindrome)    6. Novel (2 definitions)    

7. Nowhere (now + here)

Down 1. Silicon (sound silly + con)    2. Haven (have + n)    3. Seville (Isle – I + evil)

5. Levee (le + vee)

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Train Tunnel. The train's rate of speed was 75 miles per hour. When the train entered the tunnel one child had one-fifth of the tunnel to travel at 15 mph. The train caught up, nearly.

The Hiker spent 16 hours walking. At three times faster the downhill walk took only 4 hours at 4.5 mph. The trail was 18 miles long.

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