You have 24 marbles. Twenty-three of these marbles have the same weight, and one is heavier. You have a scale balance, which will compare the weight of any two sets of marbles. How many minimum numbers of weightings are required to identify the heavier marble?
Solution
1. Divide the marbles into two groups of 12 and compare the weight, and select the heavier group
2. Divide the heavier group of 12 marbles into two groups of 6 and compare the weight, and select the heavier group of 6 marbles
3. Divide the heavier group of 6 marbles into two groups of 3 and compare the weight, select the heavier group of 3 marbles
4. From the heavier group of 3 marbles, select any 2 marbles and compare the weight. If the two marbles selected weight the same the one that wasn’t selected is the heaviest. If the one of the two marbles selected weights more, then it is the heaviest.
The correct answer is therefore 4 weightings.
The correct responses were sent by:
Gene Berek; ExxonMobil Upstream Research
Brandy R. Lang, PE; Burns & McDonnell
Charles H. "Trey" Moore III P.E.; URS Corporation
Joonho Hwang, Ph.D., P.E.; FUGRO CONSULTANTS, INC.
Michael Kane, P.E.; AECOM
P.T.Kolitha Karunaratne, E.I.T.; Terracon Consultants, Inc.
Kresimir Begic; City of Houston
Christen N. Specht, E.I.T.; Texas Department of Transportation
Asyn, Jose Javier, P.E.; Fugro Consultants, Inc
Ben Eisler; INTECSEA
May Problem
Peter picked one pepper more than Paul. Pat picked one pepper more than Pam. Peter and Paul picked 10 more peppers than Pat and Pam. Peter, Paul, Pat and Pam picked 60 peppers. How many peppers did Peter pick?
Send your solutions and comments to Kishore Juluru at kjuluru@etsiteam.com Please include “ASCE Puzzle- MAY ” in the email subject. All correct responses will be recognized in the June issue.
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