mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2007-07-09, 18:11   #1
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default Variation on a Martin Gardner puzzle

You are given the task of finding counterfeit coins.

Each batch of coins you must examine is already separated into "x" piles where x>1. "x" can be an arbitrarily large number.

One of the "x" piles is contains only counterfeit coins. No other pile contains any counterfeits.

Each pile may have a different number of coins but all must have "x" or more coins.

Your only equipment is a modern one-panned scale. There is no practical limit as to how many coins you can put on the scale.

Good coins weigh exactly 30 grams. Counterfeits weigh exactly 30.1 grams. The scale must be used to discern a weight difference. Also, the good and bad coins look exactly the same.

=====================================================

How many weighings are necessary to determine the counterfeit pile? Please justify your answer.

Last fiddled with by grandpascorpion on 2007-07-09 at 18:12
grandpascorpion is offline   Reply With Quote
Old 2007-07-09, 18:47   #2
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

2×3×13×83 Posts
Default

One weighing:
one coin from pile1,2 from pile2...x from pile x.
If the weight is W grams the conterfeit pile is 10(W-15x(x+1))
David
davieddy is offline   Reply With Quote
Old 2007-07-09, 18:57   #3
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default

Yep.
grandpascorpion is offline   Reply With Quote
Old 2007-07-09, 20:12   #4
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

2·3·13·83 Posts
Default

I guess that original puzzle was:

12 coins, one of which is either lighter
or heavier than the rest.
With a two pan balance, how many
weighings to identify the counterfeit coin?
davieddy is offline   Reply With Quote
Old 2007-07-09, 20:23   #5
grandpascorpion
 
grandpascorpion's Avatar
 
Jan 2005
Transdniestr

503 Posts
Default

This was based directly on his 10 piles of 10 coins problem but that's based on a simple puzzle like the one you describe.
grandpascorpion is offline   Reply With Quote
Old 2007-07-09, 21:40   #6
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

145128 Posts
Default

Here's a variation:
how many weighings on a single pan balance to
resolve my 12 coin problem?
davieddy is offline   Reply With Quote
Old 2007-07-12, 17:12   #7
mfgoode
Bronze Medalist
 
mfgoode's Avatar
 
Jan 2004
Mumbai,India

1000000001002 Posts
Lightbulb Coins

Quote:
Originally Posted by davieddy View Post
I guess that original puzzle was:

12 coins, one of which is either lighter
or heavier than the rest.
With a two pan balance, how many
weighings to identify the counterfeit coin?


As per Martin Gardner the counterfeit coin can be identified and tell whether it is light or heavy in 3 weighings. He derives it by ternary numbers 0 , 1 , 2 and also by letters SILENT COWARD. I hope I have understood him correctly

Thanks for the reference grandpa and Davie.

Mally
mfgoode is offline   Reply With Quote
Old 2007-07-12, 18:15   #8
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

2×3×13×83 Posts
Default

Quote:
Originally Posted by mfgoode View Post


As per Martin Gardner the counterfeit coin can be identified and tell whether it is light or heavy in 3 weighings. He derives it by ternary numbers 0 , 1 , 2 and also by letters SILENT COWARD. I hope I have understood him correctly

Thanks for the reference grandpa and Davie.

Mally
I've given this puzzle countless times to
pupils as a last day of term quiz, and yet I
still have to think hard about the solution in 3 weighings.
Each weighing requires precision and/or ingenuity.
I think a mnemonic is cheating. SILENT COWARD means
nothing to me.
The thing to remember is that we have 24 options
which must be resolved in 3 tests with 3 outcomes per test.

David
davieddy is offline   Reply With Quote
Old 2007-07-12, 18:37   #9
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

194A16 Posts
Default

BTW I've been trying to reply to your
"Always an integer" post, and it quotes an
earlier thread of yours instead. Not sure
why.
Anyway the answers to your queries are:

a)x*integer is an integer because integer*integer=integer

b)see books on "crooked E".

David
davieddy is offline   Reply With Quote
Old 2007-07-12, 19:51   #10
DJones
 
DJones's Avatar
 
Oct 2006

73 Posts
Default

Quote:
Originally Posted by davieddy View Post
Here's a variation: how many weighings on a single pan balance to resolve my 12 coin problem?
For a single pan scale, I'd say 5 weighings.
Three weighings of four coins each to determine whether the odd one out is heavier or lighter, which set of four it is in, and the weight of a normal coin.
One weighing of two coins to determine which pair the odd one out is in.
One weighing of one coin to determine the odd one out absolutely.

If the weight of a normal coin is already known, then I believe you only need four weighings;
One weighing of six coins, to determine which half the odd one out is in.
One weighing of three coins, to determine a set of three with the odd one out.
Two weighings (maximum) of one coin to find the odd one out.

I'm assuming a single-pan scale is an item on which you put objects and get a weight reading. I'm clarifying that as similar puzzles to this have used unusual terminology for scales and balances.
DJones is offline   Reply With Quote
Old 2007-07-12, 20:25   #11
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

145128 Posts
Default

I think you may be right.
Goes to show that the two pan balance
(though obsolete) had its advantages!
David
davieddy is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
RIP: Martin Gardner (1914 – 2010) cheesehead Science & Technology 20 2014-10-22 11:21
Large Prime Variation of QS Sam Kennedy Factoring 9 2012-12-18 17:30
The Fischbach Prime a mersenne variation Carl Fischbach Miscellaneous Math 28 2010-07-20 06:54
Integral Variation flouran Information & Answers 6 2009-07-20 20:00
Martin Gardner sports question grandpascorpion Puzzles 4 2007-07-24 16:57

All times are UTC. The time now is 21:35.

Thu Jul 9 21:35:08 UTC 2020 up 106 days, 19:08, 0 users, load averages: 2.20, 1.72, 1.53

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.