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I have $80$ coins.
Among them, exactly one coin is lighter compared to all the others.
I was given a physical balance, suddenly.
What is the minimal number of weighings required to find the lighter coin?

Can somebody tell me what is the meaning of this question and how to solve it?

user76568
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Android developer
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  • My advice is try thinking first how you can identify the odd coin if you have 3 coins of which one weighs less. Try acchieving that in one weighing. – 5xum Jan 27 '14 at 07:57
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    The answer is not $5$. – André Nicolas Jan 27 '14 at 08:18
  • "what is the meaning of this question" Can you explain what you want? – Phira Jan 27 '14 at 09:16
  • @AndréNicolas I do not get your comment. Why should anyone think that it is $5$? – Phira Jan 27 '14 at 09:20
  • @Phira I already write there I am not able to understand meaning of this question. I ask this question here as it is ask to me in company aptitude test. – Android developer Jan 27 '14 at 09:20
  • @Androiddeveloper "Meaning" is a very vague word. You should be more specific what you want to know about this question, and what you would regard as an answer. What is the meaning of the question: "If I gave you and apple, we would have the same amount of apples. If you gave me an apple, I would have twice your amount of apples. How many apples do we have?"? Your question can be viewed as an example for ternary digits, information theory or something else. There is no "the meaning". – Phira Jan 27 '14 at 09:25
  • Actually I write that answer is 5 previously because some of my mate told me that possible answer is 5. but i edit this question and remove that answer thing.(check edit history) – Android developer Jan 27 '14 at 09:25
  • @AndréNicolas Sorry, I did not see the previous version of the question. – Phira Jan 27 '14 at 09:26
  • A more interesting question is finding the simplest solution, when given that the answer less than 5! :) – user76568 Jan 27 '14 at 09:41

2 Answers2

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First, the meaning:
In short, I believe the meaning/purpose of this riddle, when given as a test, is to asses one's inductive reasoning skills.

Life would have been a tad easier if you had an extra coin in your disposal (Cheap fella..)

  1. Take $2$ pairs of 27 coins (54 total) and compare them with the scales.
  2. a. Weighs the same? Good. Take one of the coin-conformists and add them to the 26 you have left (27 total). Now, take 2 pairs of 9 coins and compare them.
    b. Doesn't weigh the same? Better. Take 2 pairs of 9 coins from the 27 suspects and compare them.
  3. a. or b. for 2 pairs of 3.
  4. Now you have 3 left. Comapre 2 of them. One is lighter? Ponder. Both are the same? Smash the damn scale, you found the coin.

The answer is not 5

user76568
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    I came across the same question in a book. It directly gave the answer that since $3^3<80<3^4$, the answer is 4. Can this be generalized? If so, then what is the proof that dividing a group of coins into 3 groups is always the best strategy? – idpd15 Jun 15 '14 at 14:29
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A balance is a device with two pans or bowls. If you put weight A in the first pan and weight B in the second pan you can tell which is the heavier, or whether they weigh the same. A classic balance operates using gravity with a pivot point, something like a playground see-saw, and the heavier weight (if any) goes down.

In the kind of problem you have here you can assume that the pans of the scale are big enough to take any weight you happen to put in them.

With the coins, the only real chance you have of anything balancing is to put the same number of coins into each pan. Now you need to work out what you know if the coins balance, and what happens if they don't.

If you experiment a bit, you should discover the most efficient way to do this. If you had only three weighings, how many coins could you cope with.

And note that the answer to the problem is not $5$

Mark Bennet
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