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The four artisans

The four artisans

Four artisan monks with great knowledge of logic work in the monastery making clay pots. At the end of the day each craftsman had made at least one vessel and in total 11 vessels had been manufactured although no one knew how many others had manufactured.

At the end of the day they kept this conversation:

July: Did you make more pots than me, Verne?
Verne: I dont know. Did you do more than me, Dalai?
Dalai: I dont know.
The MA: AHA!

Lama was able to deduce how many vessels each made. How many vessels did each craftsman make?

Solution

Julio made one, Verne two, Dalai three and Lama five, 11 in total.

If there are 11 total vessels, so that one of them can know that he has done more than the others he must have done at least 5. This is because if he did 5 the maximum that one of the others could have done are 4 , and the other two are left with 1.

If Julio asks Verne it means that Julio has not done 5 or more because if not Julio would know that he would have done more than all. Since Julio asked this question, Verne already knows that Julio is less than 5. Knowing this information, if Verne answered "yes", that would mean Verne has finished with 4 vessels. This is because we already know that Julio does not have 5 and the maximum that another person could have done would be 4. If Verne answered “no”, that tells us that he only has 1 and could not have more than Julio. But he replies that he does not know then with this answer we know that he has 2 or 3 crafts made. Now we continue with the following statement.

Verne asks Dalai the same question. Dalai doesn't know if he has more than Verne either. Everyone already knows that Verne has between 2 or 3. Dalai would answer "no" only if he had made 1 or 2 vessels. This is because with 1 or 2 there is no way I could have done more than Verne. Dalai says he doesn't know why Dalai is still unsure if Verne has 2 or 3. Dalai can only give this answer if he has 3 vessels made.

Lama, the last to say something knows how many each one has done. He has then done at least 5. He has also heard what all the others have said and knows that Verne did 3. If Lama had 6, Dalai would have to have 3 that gives a total of 9 and 2 would be left over to divide between Verne and July. But we already know that Verne has between 2 and 3, so Lama doesn't have 6. Then, Lama will have 5, which is the least she can have. Dalai has 3 that gives us 8 and there are 3 left to divide between Verne and Julio. We know Verne has 2 or 3, so he has to have 2 to have one left for Julio.