There were many ways that you found to solve the sequence problem, but
you fell far short of the goal of 125 solvers. Mario Nigrovic found a clever algorithm to
enumerate the solutions that required only 59 hours on a 300 MHz computer. Don Todd found
a uniqueness proof that is shorter than any I have seen. Nathan Miles found a solution for
a sequence with an infinite number of terms.
WARNING: To increase the interest of our younger solvers, I have included some implied
violence in the problems for this issue.
Freddie Fly and Sally Spider are currently located at two corners
(vertices) of a room (rectangular parallelepiped) as shown in the figure. Sally is hungry
and bent on eating Freddie as soon as possible. Since she cannot fly, she must crawl on
the floor, ceiling or walls. Find her shortest crawl distance to reach Freddie for the
following cases. You may assume that Freddie is so frightened that he remains in his
corner throughout the attack. Problem 1. Her path must go through two
vertices, not including her initial corner or Fred’s corner. The room dimensions are
a = 3, b = 4, and c = 5.
Problem 2. Same as Problem 1 except replace ‘two’ by
‘one’.
Problem 3. Same as Problem 1 with no path restrictions except that she
still has not learned to fly.
Problem 4. Same as problem 3 but the room dimensions are a = x, b = y,
and c = z, with x > y > z. Your answer should depend on this inequality.
Your children with modest geometry skills and some ingenuity are
invited to submit their solutions to problems 1 and 2.
Alumni and future alumni solvers
George Kesler (1942), W.C. Soudriette (1943), Cecil Cook (1949),
Charles E. Cooper (1956), Art Sutton (1956), H. D. Brown, Jr. (1957), John Tindall (1961),
Mike Gilpatrick (1962), Joe Snyder (1962), Don Todd (1962), John Andis (1968), Dale A.
Willman (1972), Doug Bryant(1973), Paul Heller (1973), William Lipp (1973), Richard
Ditteon (1975), Nathan Miles (1976), Scott Warner (1978), Paul Gunn (1981), Mike
McCullough (1981), Larry Alldredge (1982), Mark Muri (1982), Rob Marchant(1983), Kurt
Staiger (1984), Mark Parsons (1985), Mario Nigrovic (1987), Chris Abdnour (1989), Michael
Garretson (1989), Rob Parks (1989), Chris Sloffer (1989), Dean Woodward (1989), Greg
Heimann (1990), Ben Hill (1990), Steve Keller (1990), Bob Burger (1991), Amit Bhatiani
(1992), Ric Antonini (1993), Dave Goodman (1993), Rick Mohr (1996), Ryan Scherle (1996),
Mike Pilcher (1998), Paul Gross (2003), Michael Simon (2003), and Matt Freeman (2004).
Others
Noel Moore, Jennifer Bailey, Bill Markel, James Durlacher, Michael
Munson, Mike Munson, Joe Rabinoff, and Bill Talbot.
Send your solutions of these problems to Herb.Bailey@rose-hulman.edu or to Herb Bailey,
Math. Dept., Rose-Hulman, 5500 Wabash Ave., Terre Haute IN, 47803. Note that you should
not include the box number as in previous mailings. Bailey is professor emeritus of
mathematics. |
