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 Replies: 15 / Views: 3,077 |
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Valued Member
United States
492 Posts |
If you are not familiar with Car Talk, it is a weekly radio show on NPR where callers can call in about cars and/or car repair. The hosts of Car Talk are brothers Tom and Ray Magliozzi, known on the air as Click and Clack, the Tappet Brothers. Each week they present a riddle, mystery, question, whatever you want to call it. They call it the Car Talk Puzzler. This week's puzzler concerned coins, so I thought if you're on Coin Community and you like puzzles and math, then this may be for you. You can submit your answer to the show here to try and win a $26 gift certificate to their "Shameless Commerce Division." Here is this week's puzzler: RAY: Imagine that you have in front of you fifty coins. They all look exactly alike except one of them is a fake. Because it's a fake, it weighs a couple of grams more than a real coin. So, if you had a balance scale, and you knew which was the bogus coin, you would put it on one side of the scale, a good coin on the other side... TOM: ...and it would be immediately obvious from this imbalance which was the phony coin, because it's heavier than a real coin. RAY: Right. Knowing that, you have in front of you fifty coins -- one of which is bogus. The question is, what is the fewest number of weighings on a balance scale that you need to perform to determine which coin is bogus? TOM: And, Part B of the puzzler: How can you do it in four? |
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Rest in Peace
United States
4078 Posts |
This was a great radio show. Loved to hear Click and Clack on NPR. I believe I heard they have retired. How sad and good for them with how many years doing the show?
I have no clue for the answer yet but, please let us know.
TJB17, thanks for a GREAT POST!
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Pillar of the Community
Australia
2830 Posts |
if luck were on my side, I could have in two weighings.
Without luck, the best I can work out is five weighings, for a guaranteed outcome.
I won't put up details now, as I don't want to spoil it for others.
Nice puzzle. I look forward to further posts.
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Pillar of the Community
United Kingdom
4208 Posts |
I can do it in one weighing if you give me the scale of my choice.
Otherwise, 5 is my fewest.
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Valued Member
Canada
83 Posts |
I think this is the answer for only four weighings...
Weighing #1:
Side A = 17 coins
Side B = 17 coins
Off to the side = 16 coins
If the scale is balanced, fake is in the 16 pile, otherwise it is in the heavier side of the scale
Weighing #2: (Assume worst case scenario and we have 17 coins)
Side A = 6 coins
Side B = 6 coins
Off to the side = 5 coins
If the scale is balanced, fake is in the 5 pile, otherwise it is in the heavier side of the scale
Weighing #3: (Assume worst case scenario and we have 6 coins)
Side A = 2 coins
Side B = 2 coins
Off to the side = 2 coins
If the scale is balanced, fake is in the off to the side pile, otherwise it is in the heavier side of the scale
Weighing #4: (We only have two coins left)
Side A = 1 coin
Side B = 1 coin
The heavier side of the scale is the fake coin
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Pillar of the Community
 Canada
9864 Posts |
Way to go WildYapok!
"Dipping" is not considered cleaning...
-from PCGS website
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Valued Member
United States
455 Posts |
Amazing WildYapok...good job!
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Bedrock of the Community
13014 Posts |
You could do it in 1. 1 coin on one side 1 on the other and the scale doesn't balance  |
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Pillar of the Community
Australia
2830 Posts |
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Rest in Peace
United States
4078 Posts |
Good one Wild Yapok. On the real show your answer would be randomly selected from the other winning submissions. Car Talk was an all time favorite of mine.
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Valued Member
Canada
83 Posts |
Thanks!
I'm not too bad with number puzzles - especially when I can't win a prize; the prize is too much pressure :)
Since I'm not in the States, everyone who is - and is eligible to enter the contest - is welcome to use my answer.
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Rest in Peace
United States
4078 Posts |
I am almost positive that the brothers Tom and Ray have retired. They may be doing reruns. I may be wrong.
It would not have made a difference if you lived in Canada .
Edited by bpoc1
03/03/2013 11:24 am
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Pillar of the Community
United States
1795 Posts |
Used to listen to Click and Clack all the time! Great Spot on the radio. Public Radio. I would say 2-6 weighings and you would probably have the fake coin. But thats only an educated guess.
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Pillar of the Community
United States
3486 Posts |
Oh poopies! The secret is out.
Car Talk puzzles keep me coming back week after week.
First step, slit 50 coins into 25 and 25. Weigh. Underweight are genuine.
You folks take it from there.
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Valued Member
 United States
492 Posts |
I think some of you are correct. It looks like the guys did retire: Quote:
On June 8, 2012, it was announced that after 35 years of hosting the show, the Magliozzi brothers were retiring and that Car Talk would stop producing new episodes as of October 2012, but that NPR will continue airing the show in reruns. I had no idea. I've been listening to the show not know that these are repeats. I usually get to listen to one a month if I am lucky, so the chances that I've heard a repeat are pretty slim. I guess we can't submit answers anymore, but it was a nice coin related puzzler anyway. Way to go WildYapok! |
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New Member
United States
1 Posts |
Too bad the show is a repeat -- this is the first puzzler that I've bothered to really try. I think you can guarantee to do it in 4 and hope to do it in 2 by starting with 24 coins on each side of the scale.
(The pile with the fake coin is in italics in these examples.)
The lucky route:
Weighing #1
Side 1: 24
Side 2: 24
Off the scale, possibly fake: 2
Deemed real: 0
Weighing #2
Side 1: 1
Side 2: 1
Off the scale, possibly fake: 0
Deemed real: 48
The unlucky route:
Weighing #1
Side 1: 24
Side 2: 24
Off the scale, possibly fake: 2
Deemed real: 0
Weighing #2
Side 1: 9
Side 2: 9
Off the scale, possibly fake: 6
Deemed real: 26
Weighing #3
Side 1: 3
Side 2: 3
Off the scale, possibly fake: 3
Deemed real: 41
Weighing #4
Side 1: 1
Side 2: 1
Off the scale, possibly fake: 1
Deemed real: 47
This strategy assumes that going over 4 weighings will kill you and you want to gamble on the possibility of finding the fake in 2 weighings. You are more likely to find the fake in 3 if you do:
The less risky way, also lucky:
Weighing #1
Side 1: 12
Side 2: 12
Off the scale, possibly fake: 26
Deemed real: 0
Weighing #2
Side 1: 3
Side 2: 3
Off the scale, possibly fake: 6
Deemed real: 38
Weighing #3
Side 1: 1
Side 2: 1
Off the scale, possibly fake: 1
Deemed real: 47
The less risky way, but unlucky:
Weighing #1
Side 1: 12
Side 2: 12
Off the scale, possibly fake: 26
Deemed real: 0
Weighing #2
Side 1: 9
Side 2: 9
Off the scale, possibly fake: 8
Deemed real: 24
Weighing #3
Side 1: 3
Side 2: 3
Off the scale, possibly fake: 3
Deemed real: 41
Weighing #4
Side 1: 1
Side 2: 1
Off the scale, possibly fake: 1
Deemed real: 47
Of course, if you want to risk not being able to do it in 4 steps, just pick two coins and test them against each other! :) In real life, the strategy would be driven by the cost of each weighing and the shape of the payoff curve for finding the coin more quickly. (I might be a nerd.) (I also might be wrong.)
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Replies: 15 / Views: 3,077 |
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Posted 03/02/2013 6:08 pm
