Timeline for One hat's number is the sum of the other 2. How did A figure out his hat number?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 26 at 23:06 | comment | added | Andrew Savinykh | @FlorianF have you seen now deleted answer by Servaes? I'm sorry I missed all the drama, I think that answer considered all the possibilities, would you agree? | |
| Jul 26 at 23:03 | comment | added | Andrew Savinykh | @SwissFrank, I think in this class of problems it can be safly assumed, that the participants are honest and doing their best. | |
| Jul 26 at 18:45 | comment | added | Swiss Frank | @Servaes B knows the rules don't actually give any of the players a constraint to answer if they know. No lesson can be drawn from a non-answer. I actually love the problem this problem wants to be but it's not that problem, it's sadly this problem. | |
| Jul 25 at 15:48 | comment | added | Florian F | While I believe the answer is correct, there still is the difficult question of whether we took into account all possible deductions. | |
| Jul 24 at 18:35 | comment | added | ralphmerridew | I expanded my original post a bit after Hemant's comment. | |
| Jul 23 at 22:26 | comment | added | Idran | @HemantAgarwal The rest of the answer is then just continuing this logic from there in figuring out which ratios, knowing that A and B didn't win, would have let C win immediately, and which ratios, knowing B and C didn't win after his turn, would let A win immediately. Then, since we know A's hat has 50, we can figure out exactly which ratio is possible by what hats he saw and which ratio they must've matched. | |
| Jul 23 at 22:21 | comment | added | Idran | @HemantAgarwal This sort of logic is also why B wins if the ratio is either (1,2,1) or (2,3,1). If the ratio is (1,2,1), then he can just use the same logic as A. If the ratio is (2,3,1), then since he can see A and C, he knows the ratio must be (2,X,1) with X either 1 (2 - 1) or 3 (2 + 1). And since B also knows that A didn't win immediately, X can't be 1, so he knows X must be 3 and his own hat is A + C. | |
| Jul 23 at 22:11 | comment | added | Idran | @HemantAgarwal A knows that one of the hats has the number that's the sum of the other two. If he sees that hat B and hat C have the same value X, then that means either his own hat has 0 (so hat A + hat B = hat C) or his own hat has 2X (so hat B + hat C = hat A). Since no hat can have 0, that would only leave the second possibility. Thus we know that a ratio of (2,1,1) would let A figure out his own hat's value. For any other set of numbers, he can't know without more information if his hat is |hat B - hat C| or hat B + hat C. Thus we know any other ratio wouldn't. | |
| Jul 23 at 21:21 | comment | added | user90442 | @SwissFrank ;) Though then you'd expect B not to pass, but to conclude that their number is 75. | |
| Jul 23 at 20:55 | comment | added | Swiss Frank | A may have seen two 25's on the first round and simply chose not to answer then, knowing he'd still be able to win the second round. | |
| Jul 23 at 14:04 | history | edited | ralphmerridew | CC BY-SA 4.0 |
added 324 characters in body
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| Jul 23 at 13:54 | comment | added | Hemant Agarwal | How did you figure out that for A to win the ratio is 2,1,1. For B to win the ratio is 1,2,1 or 2,3,1 ? Pls give a more detailed and intuitive answer. | |
| Jul 23 at 11:00 | history | answered | ralphmerridew | CC BY-SA 4.0 |