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A professor was a guest lecturer at a logic course for senior executives of major oil companies. She selected six male participants for this demonstration.

The professor placed fifteen 10 cent coins and fifteen 5 cent coins in six tin cups such that each cup contained the same number of coins but a different amount of money. She made six labels showing correctly how much money each cup held, but attached to each cup an incorrect label. She explained the situation to the six participants and gave a cup to each. She asked each participant in turn to feel the size of as many coins as he wanted in his own cups and announce something true about them. The only evidence each participant had was the size of the coins he felt, the incorrect label of his own cup, and the statements made by those who preceded him.

* The first man said: "I feel four coins which are not all the same size; I know that my fifth coin must be 10 cent".

* The second man said: "I feel four coins which are all the same size; I know that my fifth coin must be 5 cent".

* The third man said: "I feel two coins, but I shall tell you nothing about their size; I know what my other three coins must be."

* The fourth man said: "I feel one coin; I know what my other four coins must be."

Determine how the remaining two cups were labelled and what the total value of the money in those two cups were.

no guesses please, justify.

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A professor was a guest lecturer at a logic course for senior executives of major oil companies. She selected six male participants for this demonstration.

The professor placed fifteen 10 cent coins and fifteen 5 cent coins in six tin cups such that each cup contained the same number of coins but a different amount of money. She made six labels showing correctly how much money each cup held, but attached to each cup an incorrect label. She explained the situation to the six participants and gave a cup to each. She asked each participant in turn to feel the size of as many coins as he wanted in his own cups and announce something true about them. The only evidence each participant had was the size of the coins he felt, the incorrect label of his own cup, and the statements made by those who preceded him.

* The first man said: "I feel four coins which are not all the same size; I know that my fifth coin must be 10 cent".

* The second man said: "I feel four coins which are all the same size; I know that my fifth coin must be 5 cent".

* The third man said: "I feel two coins, but I shall tell you nothing about their size; I know what my other three coins must be."

* The fourth man said: "I feel one coin; I know what my other four coins must be."

Determine how the remaining two cups were labelled and what the total value of the money in those two cups were.

no guesses please, justify.

Thanks

The fisrt cups were labelled 25 cents and 35 cents,the total 40 cents.

Because 22.5 (5cents)-3(10cents)-1.0(5cents)-4(10c)-0.5(5c)-2(10c)-1.5(5c)-4(10c)=4.0(5c)and 2(10c)=25 cent and 35 cent

thank you

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I should mention that using 2 types of coins and 5 coins in each cup you get exactly 6 different combination (25, 30, 35, 40, 45, 50)...

The first guy said he had four coins which were not all the same but he knew what the fifth was, if the 4 coins had been 3 of one size and one of another then he'd have 4 different possibilities for the total and he couldn't guess what his fifth coin was, but if he had 2 and 2 then they'd equal 30 and he'd either have 35 or 40 cents in his cup, the only way he could've known what his fifth coin was is if his cup had "35" written on it which he knows is incorrect so his fifth coin is 10 and he had 40 cents with him (5,5,10,10,10)...

I got to the second guy but I can't make anything out of what he said, he felt four coins which are the same so he has four different possibilities (5,5,5,5,5) (5,5,5,5,10) (5,10,10,10,10) (10,10,10,10,10), the label on his cup cancels out only 1 possibility but he can make nothing out of the info he got from the first guy, so I dunno how to continue from here if I don't know how the second guy could've concluded what his fifth coin was was...

Did he have access to any other type of information? could he see what the others had on their cups? could he have been wrong?

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I should mention that using 2 types of coins and 5 coins in each cup you get exactly 6 different combination (25, 30, 35, 40, 45, 50)...

Did he have access to any other type of information? could he see what the others had on their cups? could he have been wrong?

Oh dear, I appear to have opened a floodgate of questions, some of which I will now answer, and some of which you need to answer for yourself as part of your own solution for working out the final result. While I am happy to help clarify parts of the question, I'm not going to tell you how to work out every step along the way!

getting through this problem will require you to keep track of multiple possibilities for each person and only eliminating each of them if you can conclusively prove a certain combination of constraints makes that possibility impossible. You'll also need to realise that later people can be thinking about what the earlier people have said, and make sure you've identified every possible constraint you can to eliminate the range of possible combinations each person has.

Now, let's revise the question:

"The only evidence each participant had was the size of the coins he felt, the incorrect label of his own cup, and the statements made by those who preceded him."

Now consider the following:

(a) they're not stupid

(b) they know what coins feel like, and the difference between a 5c and a 10c piece

© there is a complete set of correct labels for the cans, it's just that none of the cans have the correct label for that specific can stuck to it

(d) they can only see their own label, not anyone else's

(e) all the statements they make must be true

As with previous constraint-based questions the trick is to ask yourself which of the combinations would violate some of these constraints? Put yourself in their position and then enumerate the different possibilities - how many are legal, how many are illegal? Once you are blocked from eliminating any more possibilities, try moving on to the next person to see what they say, what could they know, what possibilities are legal for them, which combinations are not?

Lastly, some specific responses:

Q1a) Could the men tell the value of the coin by the size of the coin??

Q1b) the last man, can he tell whether the only coin he felt is a 5 cent or 10 cent ?

Q1c) For the first and second man, did he feel 4 coins separately or at once. Because if they felt the coins at once , how can they tell whether they have the same size or not ?

Q1d) The second man said: "I feel four coins which are all the same size; I know that my fifth coin must be 5 cent". Does that mean the first four coins are different from the fifth?

Q1e) when the second man states that he can feel four coins of the same size, with his fifth coin being a 5 cent piece, is this saying that the other four coins must be 10 cent pieces or could they also all be 5 cent pieces? similarly with the third and fourth men, when they state that they know what the other three and other four coins are, respectively, does this infer that these coins are of the same value, or merely that they know which coins they must be by some logical process.

A1) If they physically touch any coins they have perfect knowledge of the coins they touched. They're CEOs, I think it's safe to assume they've touched a couple of 5c and 10c pieces in amongst the millions of dollars they've already made. But they only have direct knowledge of the coins they physically touched, so if they make any other claims then they *must* have deduced that truth from what they have just touched, what they can see and what they have heard up until now. Also, semi-colons are strong separators, so the two clauses should be read completely separately rather than with some kind of verbal inflection. So again, deduction is at play rather than them lying about touching the extra coins as well.

Q2) Does the label say exactly which coins are in the tin or only the total amount of money in the tin? i.e. "One 5c, four 10c" or "45c"?

A2) It doesn't say 'how much of each coin', it says 'how much in each tin', so it's just the aggregate total.

Q3) Just a little confused... Does each person announce their true statement then their false label?? eg First man: "(True statement);(False label)"

A3) Uh, I think you misunderstand. Both clauses are always true, but they may have derived it by combining information from a variety of sources. The word 'label' isn't intended as an abstract linguistic component - it literally refers to an actual sticky thing with a number written on it.

Q4) I havent finished all my modelling yet but have a solution that satisfies the claims made by the first four men assuming that they deduce their cups contents based on the labels on the other mens cups and what the men who have spoken before them say. However this particular solution has two cups remaining that do not correspond to the amount of money on either of the two remaining labels (i.e each label could go on either cup). Is this a sufficient solution or is it required that the final two cups need specific labels on each of them (is there one unique solution).

A4) They cannot see the labels on the other cups. You also appear to be describing an illegal solution, since "everything matches perfectly, except for the things that don't match at all". Having multiple solutions isn't the same thing as having invalid solutions (since all puzzles have lots of invalid solutions!), so you might want to check that again with a fine-toothed comb...

Q6) I am also confused. If every cup is labeled incorre correctly, doesn't that mean that sinply the last two cups are just labeled incorrectly? What are the constraints to the labels. Was evey cup initally labeled correctly nad then the labels were swapped? Or are there labels saying a cup has $100.

A6) Yes, the labels are wrong, but you need to tell me what those labels say - actual numbers like '20c' or '75c'. As is stated in the question - the actual values on the labels exist... and correctly and uniquely to a particular can, it's just that they are not on their matching can. None of the labels are invalid, no $100 or -$24 or $0.314159. Your shuffling suggestion is fine, just so long as you understand the labels were shuffled without anyone knowing which label came from or went to which can.

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The last 2 cups have the 30 and 35 cent labels and have a combined value of 75 cents. Explanation to follow.

Disregard the above. I crossed my wires right from the start. Starting over :P

Edited by Tuckleton
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First, I'm going to name all the possible combinations to simplify the explanations.

1: 5,5,5,5,5 (25)

2: 5,5,5,5,10 (30)

3: 5,5,5,10,10 (35)

4: 5,5,10,10,10 (40)

5: 5,10,10,10,10 (45)

6: 10,10,10,10,10 (50)

The first CEO says that he has felt 4 of his 5 coins and now knows what the last one has to be. But there are 2 possibilities for his last coin. How does he know? Well, he knows that his label must be wrong so one of the possibilities must be represented by his label so the other must be true! For example, say he feels 1 nickel and 3 dimes, he might have 4 or 5 (from above). But then he notices he has label 4. Since this must be wrong he knows he has 5! We can use this to list what is possible based on what we know so far.

CEO A has one of the following:

3 with a label saying 2

4 with a label saying 3

5 with a label saying 4

Moving on. CEO B has 4 of the same and says he knows his last coin is a nickel. Same situation as above.

CEO B has one of the following:

1 with a label saying 2

5 with a label saying 6

CEO C gives us a challenge. He has felt 2 coins, won't tell us about them and claims to know his other 3. How can this be? Let's examine what's possible:

CEO C felt 2 nickels. He could have 1,2,3 or 4

CEO C felt one of each coin. He could have 2,3,4 or 5

CEO C felt 2 dimes. He could have 3,4,5 or 6.

We can assume he's come to the same conclusions about A and B that we have. So what he has felt and seen combined with that knowledge must have allowed him to come up with a unique answer. The only way to do this is if he has label 2. If he sees label 2 that means that CEO B must have seen label 6 and have had 5. Then CEO A could not have seen label 2 nor could he have 5 so he must have seen label 3 and have 4! Now, the only way this knowledge could lead CEO C to a single possibility is if he had felt one of each kind of coin so he must have 3.

To recap, we now know:

CEO A has 4 with a label saying 3

CEO B has 5 with a label saying 6

CEO C has 3 with a label saying 2

Now, CEO D only feels one coin and claims to know his other 4. So what's possible:

CEO D felt a nickel. He could have 1,2,3,4 or 5

CEO D felt a dime. He could have 2,3,4,5 or 6

But we can assume that CEO D knows the same things we have deduced. So this narrows it to:

CEO D felt a nickel. He could have 1 or 2

CEO D felt a dime. He could have 2 or 6

But CEO D claims he knows what he's got. So his label must be informing him of what to eliminate. Since labels 2,3 and 6 are all already out there, he must have felt a nickel and seen label 1 informing him that he has 2.

We've eliminated labels 1,2,3 and 6 and accounted for 2,3,4 and 5 in the cups. This leaves labels 4 (40) and 5 (45) and 1 (25) and 6 (50) in the cups for a total of 75 cents.

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First, I'm going to name all the possible combinations to simplify the explanations.

1: 5,5,5,5,5 (25)

2: 5,5,5,5,10 (30)

3: 5,5,5,10,10 (35)

4: 5,5,10,10,10 (40)

5: 5,10,10,10,10 (45)

6: 10,10,10,10,10 (50)

The first CEO says that he has felt 4 of his 5 coins and now knows what the last one has to be. But there are 2 possibilities for his last coin. How does he know? Well, he knows that his label must be wrong so one of the possibilities must be represented by his label so the other must be true! For example, say he feels 1 nickel and 3 dimes, he might have 4 or 5 (from above). But then he notices he has label 4. Since this must be wrong he knows he has 5! We can use this to list what is possible based on what we know so far.

CEO A has one of the following:

3 with a label saying 2

4 with a label saying 3

5 with a label saying 4

Moving on. CEO B has 4 of the same and says he knows his last coin is a nickel. Same situation as above.

CEO B has one of the following:

1 with a label saying 2

5 with a label saying 6

CEO C gives us a challenge. He has felt 2 coins, won't tell us about them and claims to know his other 3. How can this be? Let's examine what's possible:

CEO C felt 2 nickels. He could have 1,2,3 or 4

CEO C felt one of each coin. He could have 2,3,4 or 5

CEO C felt 2 dimes. He could have 3,4,5 or 6.

We can assume he's come to the same conclusions about A and B that we have. So what he has felt and seen combined with that knowledge must have allowed him to come up with a unique answer. The only way to do this is if he has label 2. If he sees label 2 that means that CEO B must have seen label 6 and have had 5. Then CEO A could not have seen label 2 nor could he have 5 so he must have seen label 3 and have 4! Now, the only way this knowledge could lead CEO C to a single possibility is if he had felt one of each kind of coin so he must have 3.

To recap, we now know:

CEO A has 4 with a label saying 3

CEO B has 5 with a label saying 6

CEO C has 3 with a label saying 2

Now, CEO D only feels one coin and claims to know his other 4. So what's possible:

CEO D felt a nickel. He could have 1,2,3,4 or 5

CEO D felt a dime. He could have 2,3,4,5 or 6

But we can assume that CEO D knows the same things we have deduced. So this narrows it to:

CEO D felt a nickel. He could have 1 or 2

CEO D felt a dime. He could have 2 or 6

But CEO D claims he knows what he's got. So his label must be informing him of what to eliminate. Since labels 2,3 and 6 are all already out there, he must have felt a nickel and seen label 1 informing him that he has 2.

We've eliminated labels 1,2,3 and 6 and accounted for 2,3,4 and 5 in the cups. This leaves labels 4 (40) and 5 (45) and 1 (25) and 6 (50) in the cups for a total of 75 cents.

Congrats mate, you got it !!! well done (-;

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Congrats mate, you got it !!! well done (-;

So I finally looked at the spoiler because I've been beating my head against my desk trying to figure out which label was on which of the final two cups. Then I realized I simply can't read :( - I guess I missed the "total value" and remaining two labels bit. Arrgh!! Great little puzzle - thanks.

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So I finally looked at the spoiler because I've been beating my head against my desk trying to figure out which label was on which of the final two cups. Then I realized I simply can't read :( - I guess I missed the "total value" and remaining two labels bit. Arrgh!! Great little puzzle - thanks.

lol , at least you tried, I am sure if you looked at the part you 've missed, you would have done it, but he did it nicely, with perfect layout, thanks for participating! :thumbsup:

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