Old and New Mathematical Puzzles
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The first eight of these "Old and New Mathematical Puzzles," which appeared in the 1989 edition of The Old Farmer's Almanac, are fairly simple to figure out. None have a Difficulty rank of greater than three. They also happen to be the only ones available, because I neglected to scan the second page with problems 9 through 15 - and I cannot find the hard copy. Oh well, the others would have been more trouble than they're worth for most people. In all the years I have worked those problem sets, rarely did I bother putting the thought required to solve the Difficulty 4 and Difficulty 5 challenges. Admittedly, most were too baffling for me. I know some of you out there in the RF Cafe audience can do them with the greatest of ease. Anyway, good luck to you on these. Old and New Mathematical PuzzlesBlanton C. Wiggin, Puzzle Editor Here are 15 classical, original, and timely puzzles for 1989 from our readers. There should be something to interest everyone, and we hope they are challenging. Everyday common sense and a little agility are all you'll need; you won't need calculus, computers, alertness to tricks, or specialized knowledge, though these are sometimes helpful. Some puzzles may require a chart or data from your local library. We will award one prize of $50 for the best set of solutions to puzzles 12 through 15 received before February 1, 1989. The answers to these four are omitted here. We use a point system to judge the prize set. A basic, unadorned, correct answer is 20 points. For a thorough analysis, an elegant or novel answer, up to 5 points extra. Numerical errors lose only 2 or 3 points, if it is clear that the method is understood. Explanations and Prize-Set Answers will be sent after June 15 to anyone sending 50ยข and a self-addressed stamped envelope to "Puzzle Answers," The Old Farmer's Almanac, Dublin, NH 03444. We will also pay $15 for any original puzzles we use in The Old Farmer's Almanac for 1990. Closing date for submissions is February 1, 1989. Entries become the property of Yankee Publishing Incorporated and cannot be acknowledged or returned. We are happy to find that a number of teachers, grades 4 through college, use our puzzles in their classrooms. We've enjoyed talking to some of these college classes. Some of this year's puzzles submitted by students are noted. The 1988 winner is George Hall, Tucson, Arizona, a frequent entrant, with a masterful entry, scoring 98.5. Hall included clear explanations, background material, and interesting asides. In a year of unusually good answers, runner-up is Tina Virzi, Plattsburgh, New York, with 95.5! She was followed by Arthur Loepp, Kansas City, Missouri, 95.25, and for fourth, a tie between last year's winner, Bob Symons, Waterloo, Ontario, and Bob Matthews, West Hartford, Connecticut, 95. Congratulations to all! Have fun with these 1989 puzzles, and send your answers early for puzzles 12-15. Please use a separate sheet for each puzzle or answer. Be sure to put your name and address on each sheet. Good luck! Answers appear on page 219. 1. Six Stix Difficulty: 1 a) Arrange 6 toothpicks so that each pick touches every other pick. b) Rearrange the same 6 to form exactly 4 - only 4 - equilateral triangles. Ruth Dykstra Bussey, Iowa 2. Better Barns Difficulty: 1 Farmer Allen's 2 barns were built 100 years apart. Their 1989 ages multiplied together equal 1989! When were they built? Mary E. B. Nightingale Brookline, New Hampshire 3. Simple Estimates Difficulty: 1 a) A man calculated the square root of2 (actually 1.41421... ) with an error of about 1 percent by simply dividing two small numbers in his head. How did he do it? The Old Farmer's Almanac 1966 b) The Greeks calculated π (actually 3.14159... ) in the same way. What were their numbers? Patty Nagy Huntington, L.I., New York 4. End States Difficulty: 2 We're not looking for stability at the end of a nuclear decay chain, just some ordinary geography. a) Which American state is southernmost, northernmost, westernmost, and which is easternmost? b) OK? Now how about the lower 48? c) Fair enough. What about Canadian provinces? d) You are viewing a lovely sunset. On the other side of the earth, at your antipodes, people are watching the sunrise. What is their latitude and longitude? Fran Loutrel Wellesley, Massachusetts 5. Time of the Pharaohs Difficulty: 2 Using 455 cubic blocks, an Egyptian apprentice constructed a small, square, solid pyramid to earn his diploma. Every block in each level took an equal amount of time to place, but at each higher level, the time per block doubled. He labored 1879 hours to complete the pyramid. How much time did he expend placing the single block at the top? Jack Tumath Plymouth, Michigan 6. Grove of Trees Difficulty: 3 "I am constrained to plant a grove to satisfy the maid I love. This ample grove must be composed of nineteen trees in nine straight rows. And in each row five I must place, or ne'er expect to see her face. Ye men of art lend me your aid to try to please this lovely maid." How would you arrange the trees? Cason D. Brinson circa 1850 Garland W Brinson Sneads Ferry, North Carolina 7. Seattle Trip Difficulty: 3 In this 100th anniversary year of Washington State, Pete Yakima will return to his hometown 3,500 miles from Miami, Florida. He leaves at sunrise October 25, doesn't touch or wind his electric watch, which keeps perfect time, and drives continuously at a leisurely rate of 270 miles a day, arriving before the anniversary date. What time will his watch read at moonset in Seattle on the day he arrives there? Doreen Rowe Collinsville, Illinois
Difficulty: 3 Little Tommy caught 2 tadpoles and put them in a tank. When they were still, he looked down into the tank and saw View D: Missing the rest of Puzzle 8 and 9-15.
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Answers to Old and New Mathematical Puzzles
b. 3 are above the table. 2. 1872 and 1972 3. a. 10/7 b.22/7 4. a. South: Hawaii; North, West, and East: Alaska. (Aleutians are partly in high E. longitude.) b. South: Florida; North: Minnesota; West: California; East: Maine. c. South: Ontario; North: Quebec; West: British Columbia; East: Newfoundland. d. Lat.: Same as yours, opposite pole. Long.: 18° minus yours, opposite direction.
6. See drawing to right. 7. No moonset that day, despite all corrections. (His watch will read approximately 7:16 A.M., EDT, Nov. 7, on arrival at 3:16 A.M. in Seattle.)
**** Answers to 9-11, Puzzles missing 9.60, up to 120 crates of oranges to B. 10. a. 78' b.91 11. 1 12-15 and Bonus. Prize Set. See in-structions on page 198.
Posted March 27, 2024 |
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8. Double Vision 
