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Ponder This

June 2002

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Ponder This Challenge:

This month's puzzle is based on a suggestion of Alex Marmer. It's another coin-weighing problem.

You are given a scale with two pans. This scale will report the difference, in grams, between the masses on the two sides, as well as telling you which side is heavier. So if you place 25 grams on the left pan and 27 grams on the right, you find out that the right side is heavier by 2 grams.

You are given N bags of coins, apparently identical. Each bag contains ten coins. Exactly one bag is full of counterfeit coins, and the rest are full of honest coins . All honest coins are equally massive, all counterfeit coins are equally massive, and counterfeit coins are heavier than honest coins. But you don't know beforehand the masses of honest coins or of counterfeit coins.

You are given the opportunity to make three weighings on your scale, after which you must decide which bag is bogus. You're allowed to open the bags and use an arbitrary number of coins from each bag, if that helps; just keep track of where you got the coins.

What is the largest value of N which can be accommodated?

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Challenge: 06/03/2002 @ 9:00 AM EST
Solution: 06/28/2002 @3:00 PM EST
List Updated: 06/26/2002 @3:00PM EST

People who answered correctly:

Jacques Willekens (6.5.2002 @ 10:00 AM EDT)
Michael Malak (6.5.2002 @ 10:00 AM EDT)
Chris Wilson (6.5.2002 @ 10:00 AM EDT)
Chu-Wee Lim (6.5.2002 @ 11:45AM EDT)
Graeme McRae (6.6.2002 @ 10:30AM EDT)
Maxim G. Smith (6.6.2002 @ 10:30AM EDT)
Christopher Howe (6.6.2002 @ 10:30AM EDT)
Robert J. Sides (6.10.2002 @ 10:00AM EDT)
Ervan Darnell (6.10.2002 @ 10:00AM EDT)
Ed Sheppard (6.10.2002 @ 10:00AM EDT)
John G. Fletcher (6.10.2002 @ 10:00AM EDT)
John McGee (6.10.2002 @ 4:00PM EDT)
Christie Bolton (6.12.2002 @ 1:30PM EDT)
Sunil Srivastava (6.14.2002 @ 10:30AM EDT)
Dan Ungureanu (6.14.2002 @ 10:30AM EDT)
Piotr Zielinski (6.14.2002 @ 10:30AM EDT)
Ashish Mishra (6.17.2002 @ 9:30AM EDT)
Sorav Bansal (6.17.2002 @ 9:30AM EDT)
Varun Sagar Malhotra (6.17.2002 @ 1:30PM EDT)
Itsik Horovitz (6.20.2002 @ 10:00AM EDT)
Andy Lowry (6.20.2002 @ 10:00AM EDT)
Ish Dham (6.20.2002 @ 10:00AM EDT)
Nagendra (6.20.2002 @ 10:00AM EDT)
David McCabe (6.20.2002 @ 10:00AM EDT)
BV Vaidyanath (6.20.2002 @ 10:00AM EDT)
Alex Wagner (6.20.2002 @ 10:00AM EDT)
Sarang Aravamuthan (6.21.2002 @ 10:00AM EDT)
Doug Scripture (6.21.2002 @ 10:00AM EDT)
Shmuel spiegel (6.21.2002 @ 10:00AM EDT)
José Manuel Ezquerra (6.21.2002 @ 10:00AM EDT)
Vince Lynch (6.25.2002 @ 10:00AM EDT)
Adrian Fernandes (6.25.2002 @ 10:00AM EDT)
Stephen Martin (6.25.2002 @ 10:00AM EDT)
Thomas Russo (6.25.2002 @ 10:00AM EDT)
Peter Bennett (6.25.2002 @ 2:00PM EDT)
Mitchell A. Kaplan (6.26.2002 @ 2:00PM EDT)
Divyesh Dixit (6.26.2002 @ 3:00PM EDT)

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