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Ponder This

May 2001

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Ponder This Challenge:

This month's puzzle, like many others, traces its sources to Martin Gardner (Mathematical Carnival).

PART A:

We are in a rowing boat on a circular lake, starting at the center. At the edge of the lake is a mean goblin who wants to eat us; and if he catches us, he will do so. The goblin can't swim and won't go into the lake (and doesn't have a boat!) but he can run k times as fast as we can row.
(We'll discuss the parameter k later.)

We, however, can run significantly faster than the goblin can, so if we are able to reach a point at the edge of the lake without the goblin being there, then we will be able to escape.

Will we be able to escape or are our only options to be marooned forever on the lake or to be eaten by the goblin?

The answer depends on the parameter k.
There is a threshold T, such that if k<T then we can escape, and if k>T the goblin will eat us. Find the threshold T to six digits.

PART B:

Why is the goblin called Jimmy?

Posted May 8th: Clarifications and Hints:

The correct answer is not PI=3.14159..., nor is it PI+1.

Even if it were, PI to six digits is not 3.142857. (That's the six-digit approximation to 22/7, but PI is not quite 22/7.)

Part B is there mostly for fun, but its answer relates to the correct answer to Part A.


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Challenge: 05/01/01 @12:00 PM EST
Solution: 05/31/01 @05:00 PM EST
List Updated: 05/31/01 @05:00 PM EST

People who answered correctly:

Krishna Kumar (05.01.2001 @ 3:38 PM EDT)

Saibal Mitra (05.01.2001 @ 5:26 PM EDT)
Henry Bottomley (05.01.2001 @ 7:27 PM EDT)
Bill Schwennicke (05.01.2001 @ 8:53 PM EDT)
Alexey Vorobyov (05.02.2001 @ 4:17 PM EDT)
Colin Bown (05.02.2001 @ 5:32 PM EDT)
Vince Lynch (05.06.2001 @ 9:07 AM EDT) *
Sunil Srivastava (05.07.2001 @ 5:47 PM EDT)
Michel Jacquemin (05.08.2001 @ 8:16 AM EDT)
Arjun Viswanathan (05.08.2001 @ 9:53 AM EDT)
Amit Elazari (05.08.2001 @ 11:18 AM EDT)
Steve Walter (05.08.2001 @ 1:12 PM EDT)
Marian Olteanu (05.08.2001 @ 2:10 PM EDT)
Sriram Thiagarajan (05.08.2001 @ 2:18 PM EDT)
Derek Kisman (05.08.2001 @ 5:43 PM EDT)
Jacques Willekens (05.09.2001 @ 9:42 AM EDT)
Douglas Schrag (05.10.2001 @ 9:15 AM EDT)
Michael Malak (05.11.2001 @ 10:46 AM EDT)
Tjinder Singh Manku (05.10.2001 @11:10 AM EDT)
Ionel Santa (05.11.2001 @ 8:57 AM EDT)
Jean Flies (05.11.2001 @ 11:23 AM EDT)
Bednarik Jozef (05.14.2001 @ 10:05 AM EDT)
Sridhar Srinivasan (05.14.2001 @ 6:44 PM EDT)
Ether Jones (05.14.2001 @ 9:08 PM EDT)
Jeff Little (05.17.2001 @11:55 AM EDT)
Shankar Venkataramani (05.17.2001 @ 1:41 PM EDT)
Dharmashankar Subramanian (05.17.2001 @ 3:36 PM EDT)
Victor Chang (05.17.2001 @ 8:48 PM EDT) *
Prithu (05.19.2001 @ 1:11 PM EDT)
Paul Kahler (05.22.2001 @ 9:56 AM EDT) *
Adam Daire (05.23.2001 @ 2:44 AM EDT) *
Andoni Alexandr (05.25.2001 @ 5:34 AM EDT)
Walter Isidro (05.27.2001 @ 2:38 AM EDT) **
Dave Biggar (05.27.2001 @ 8:53 PM EDT)
Holiday's Cafe (05.29.2001 @ 1:29 PM EDT)
Ross Millikan (05.29.2001 @ 2:33 PM EDT)
Alan Skelley (05.30.2001 @ 5:58 PM EDT) *
Yuriy Groysman (05.31.2001 @ 8:08 PM EDT)

* Respondent also answered part B correctly
** Respondent only answered part B correctly


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