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Bailey Challenge brings us to our census
I was truly impressed with your outpouring of outstanding solutions to the counterfeit coin problem. The problem was quite popular in England in the early 40s. It was suggested that it be dropped in leaflets over Germany to sabotage their war efforts by sidetracking their scientists into wasting time on the solution.
The winner of the best in the show was Andy Craig 91 with a 2 ft. by 3 ft. multicolored CAD presentation. A few of you gave solutions with the three weighings prescribed in advance. That is, the placement of coins in subsequent weighings does not depend on the results of the prior weighings. My computer and I have found 304 distinct solutions of this form. One difficulty is in deciding how to define distinct.
Retirement is very enjoyable but I worry about growing old. My therapist tells me to take my aging problems out of the closet so here they are. In PROB 1, the ages are expressed as integers rounded down. In PROB 2, the ages need not be integers.
PROBLEM 1.
The exchange between the census taker and the mother of three daughters went like this: "I wont tell you their ages but I will say that the product of their ages is 72 and their sum is equal to my house number that you see there." "Thats not enough information. Give me another hint." "Well, my eldest daughter likes strawberry ice cream." "Thank you, now I know their ages." How old were the daughters?
PROBLEM 2.
The combined ages of Mary and Ann are 44 years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann.
My grammar checker told me that the above sentence is very long and may be hard to understand. I wrote back that that was the purpose of the sentence. Sam Loyd was one of the great puzzle writers. PROB 2 is one of his favorite age puzzles. I solved this problem in my youth and at the time I counted this as one of my great accomplishments. His book, Sam Loyd And His Puzzles, is still being reprinted and I would recommend it for you and your mathematically inclined offspring.
The solvers of the coin problems are listed below.
Dwight Heath (43), Richard Mott (43) Bob Bannister (46), Orville Stone (48), Cecil Cook(49), Folker A. Schmidt (49), Charles Hirschfield (54), John Chinn (56) Charles Cooper (56), Art Sutton (56), Bill Fenoglio (61), Bill Remmel (61), John Tindall (61), Donald Todd (61), Ron Danilowicz (63), Chuck Divine (67), Tom Winenger (69), Bill Heeter (70), Allan Mahler (71), Wolfgang Pelz (71), Charles Doty (72), Daniel Pate (73), Mark Bailey (76), Mike Dominik (76), Dave Shirley (77), Roger Burger (79), Scott Bagwell (80), Robert Kaminsky (80), Joe Farrell (81), Jeff Nadeau (83), Chuck Hastings (86), John Hoffman (87), Chris Abdnour (89), Greg Heimann (90), Dennis Quimby (90), Andy Craig (91), Bob Burger (91), Paul Kimmerele (91), Todd Anderson (92), Greg Hall (92), Mark Young (94), Joe Coons (95), Darby Kline (95), Breck Schmidlofer (95), Meghan Shilling (01). Others: James Durlacher, Tisha King, Jim Wollscheid, Ken Farrell and Brad Divine.
by Herb Bailey
Professor Emeritus of Mathematics
Send solutions to Herb Bailey, Rose-Hulman, 5500 Wabash Ave., Terre Haute, Indiana 47803 or contact him via e-mail at herb.bailey@rose-hulman.edu
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