Four BoxesBelow are samples of the explanation of choices from respondents. Responses were interesting in that many explanations were very convincing in a particular selection, but in their overall persuasiveness began to reveal the intractable "what if" black hole that could easily be used to argue for equal distribution of choices among the four boxes. Hide (A1): When making guesses, people very rarely pick the first option. Thus, hide it in box 1. [m, 19] The first box seems the least likely to be picked by Pat. B is obvious, but too obvious so it may be picked. The 4th A is the farthest from B so instinctively it may be picked. The 3rd A is between these two boxes and draws more attention than the First A. Therefore, the 1st A seems the most likely not to be picked. [m, 35] Find (A1): It wouldn't be B, as that's just too obvious (or is it?) I guessed box 1 as noone ever seems to pick the first answer for anything, so it would be that one (knowing my luck) [f, 21] The only possible basis for anything other than random choice would be an inference about Sam's psychology. How would he choose, given that he can see the labels as well as I can. He might decide not to put it under the 'B' box simply because that's too obvious. On the other hand, he might put it precisely there because, if I chose a different box, that would be just that much more funny. Lacking any other information, I decided: 1) 2 is too obvious. 2) 3 is also in the middle, so too obvious. 3) 4 is the most distant from 2, so too obvious. 4) Therefore, 1 is the least distinguished. So, I picked 1  even though I really have no confidence in any of these inferences at all. [m, 42] Hide (B): Surely, Pat will not guess the only box that is labeled differently, box 2. sometimes the most obvious place is the most conspicuous because it's too obvious for suspect. [m, 20] Here is where having a psychologist for a husband messes with my answering this. I would say Sam would hide the money in B, because it's too obvious a location. If Pat thinks about it at all, Pat will probably pick one of the As. [f, 28] Find (B): If I was Sam, I'd put the money in B under the assumption that Pat would think B was the most obvious, and therefore the least likely, choice. Of course, this is under the assumptions that Pat is a relatively bright person, but not one whose studied interdependency problems (i.e. game theorist, CIA operative, etc), and that Sam is relatively greedy. [m, 29] They want you to think its not in B but it really is. They try to trick you. [m, 15] Hide (A2): Box 2 differentiates itself and draws attention. Boxes 1 and 4, on either end, may naturally draw attention as well. Box 3 seems least suspicious even if each box has a statistically equal chance 1:4 of being chosen. [m, 23] 2 is too obvious, which makes some avoid it. But in some cases might make you pick it, just because it's SO obvious. 1 would be the next to worst choice based on the location of the 'obvious' 2. 4 is less obvious so has potential, but it's on the end, so again, it's too obvious. So, I would put it in box 3. [f, 44] Find (A2): Box 1 and 4 are on the end and are more obvious choices for Pat. Box 2 is different and also a natural choice. Therefore Sam would put the money in box 3 as it is a less obvious choice out of the four, being the same letter and not on the end of the row. [f, 18] Since there doesn't seem to be any 'logical' solution, a random logical solution is that box 3 has a letter that is wrong if you wanted to spell ABBA. Since the other letters are correct for ABBA, box 3 is the one most unlike the others and therefore most likely to attract the attention of Sam. :) [m, 27] Hide (A3): Box 2 was a tempting choice, but the likelihood someone else would guess that box because it's different than the others would probably be high. I chose the last box because if it were me guessing, box 4 would be my last guess. If I knew more about Pat and the way he thinks, I might have chosen differently. [f, 38] We read left to right. I consider the first box an obvious choice in addition to B, simply because it's different. I suggest far right as being the least likely because it is last, and because it's one of three like it. [m, 24] Find (A3): Most people will assume (often unconsciously) that the money is hidden between the end boxes, 'covered' by them. Therefore they will go for a middle box, and as B stands out as different to the other three A boxes, will most likely go for it as the most attractive option. As Sam has evidently run this game before, and it is not a random placement of the money, then choosing notB, one of the end boxes, and the one farthest away from B appears to be the sensible choice. [M, 30] B seems a little too obvious (which is why the money should probably be ther after all). Either of the A's bordering B just seem too convenient. [m, 24] I hope you're semiconvinced that there is good reason to hide it in any of the four boxes, and it is this overall persuasiveness that leads to the "what if" blackhole scenario, and several respondents argued that the choices would be equally distributed among the four boxes: Completely random guess. I don't know Sam so I can't bring any reasoning to bear on the question, and even then the game of second guessing the competition again makes it completely random. [m, 38] There is a 25% chance to hit the correct box, regardless the name of the box. Sam can hide the money in any of the boxes without restrictions, so its only luck to choose the correct box. [m, 35] Random choice. There is an equal chance for the money to be in any of the boxes. (At least that's what I >think<) [m, 46]
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