"There space twelve(12) guys on one island, eleven(11) weigh precisely the very same amount, yet one of lock is contempt lighter or heavier,
(Rephrased for clarity, listed below is a verbatim transcript the "Holts" dialogue)
"There room twelve guys on one island, eleven weigh exactly the same amount, but one of them is slightly lighter or heavier, girlfriend must figure out which. The island has no scales, however there is a see-saw; the amazing catch, you deserve to only usage it 3 times."
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riddle logical-deduction weighing
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There space 24 feasible situations (the different man can be any type of of 1-12, and he have the right to be heavier or lighter). For this reason we should log224 bits of info to fix the puzzle. You have the right to weigh 3 combinations of men on the see-saw. Each weighing can provide 3 possible answers: left side heavier, right side heavier, or both sides equal. Hence in principle we can obtain log227 bits native the 3 comparisons. So in principle, we should be able to solve the problem. The key to this problem is making sure all three output worths (left next heavier, right side heavier, two sides the same) are feasible and much information in virtually every to compare you execute so the we deserve to eek log224 bits the end of the comparisons. Keep in mind that this means that the first comparison should yield much more than 1 bit of information. This suggests we shot maximizing the lot of info we can get from the an initial comparison, by make all 3 outcomes same likely. To compare (1,2,3,4) come (5,6,7,8) does precisely this. Comparable logic will assist us style all further comparisons.
Here is one solution:
Number the males 1,2,3...12. Very first weigh 1,2,3,4 versus 5,6,7,8. Among two things will happen:
1) They room equal. Now we recognize that the different man is among 9,10,11,12. Weigh 9,10,11 versus 1,2,3. If these are equal, the different man is 12. Sweet 12 against 1 to uncover out even if it is 12 is heaver or lighter. If the 9,10,11 differs from 1,2,3, then weigh 9 versus 10. If they are the same, the different man is 11, and also he is heavier if 9,10,11 was heavier than 1,2,3 and he is lighter if 9,10,11 to be lighter than 1,2,3. If 9 and 10 space different, the various man is the lighter the the 9,10 comparison if 9,10,11 to be lighter 보다 1,2,3, (and that is lighter); the different man is the heavier of the 9,10 compare if 9,10,11 was heavier than 1,2,3 (and the is heavier).
2) They space different. Without loss the generality mean that 1,2,3,4 is heavier 보다 5,6,7,8. (We could always relabel the males so the this is true). We recognize 9,10,11,12 all weigh the same.
Weigh 1,2,5,6,7 against 8,9,10,11,12:
a) If 1,2,5,6,7 is heavier, climate either 1 or 2 heavier, or 8 is lighter. Weigh 1 versus 2. If they room different, the more heavier of the two is the one we are looking for (and heavier). If they are the same, 8 is the one we are searching for (and lighter).
b) If 1,2,5,6,7 is lighter, then one of 5,6,7 is different and lighter. Sweet 5 against 6. If they are different, the lighter of the two is the one we are trying to find (and lighter). If they room the same, 7 is different (and lighter).
c) If they are the same, then one of 3,4 is different. Weigh them against each other. The one who is heavier is the different man (and heavier).