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MIT student blogger Bryan O. '07

Just 5 Days Left! by Bryan

Mystery Hunt begins in 5 days.

Until Mystery Hunt 2006!!!

Here’s a little puzzle to get you inspired courtesy of my friend Pete:

100 folks are caught on an island by cannibals and put to the following challenge: Each shall get one hat of either black or white (unbeknownst to them). Then, they will be asked in succession what color they believe is on their head. If they get it wrong, they are promptly eaten with a side of salad. Otherwise, they are set free.

Note: They are not allowed to talk to one another once the hats are on their heads; however, they are allowed to devise a strategy before the hat doling-out begins.

So the question is: How can the group guarantee that 99 of them survive with a foolproof strategy?

If you’re interested in remotely joining our team, just email me at [email protected].

Ciao for now.

IAP starts tomorrow.

7 responses to “Just 5 Days Left!”

  1. Teck Lee says:

    Assuming they’re allowed to communicate non-verbally (you only specified “no talking”)…

    Line them all up. When it’s a folk’s turn, the person behind him will tap his left shoulder if the hat is black or tap his right shoulder if the hat is white. This way, everyone knows what color his/her hat is except for the last guy, who is folk #100. S/he can guess, but no matter what, 99 of them survive. This, of course, assumes that everyone is selfless and only thinks of others, especially the last guy. Poor dude.

    It would seem like there are a lot of solutions.

  2. Adam says:

    I thought basically the same thing. The only difference I had would be to tap only one shoulder, but tap it once for white and twice for black.

    Same idea really though.

    The key to find here, and really think about, is a way to do it without any communication whatsoever…

    Like maybe, taking the hat off and looking at it. The directions never said they couldn’t do that.

  3. Wenhao Sun says:

    *That’s terrible ‘wrath’ of my fork.

    No really, it’s quite scary.

  4. Wenhao Sun says:

    Hahahhaa, good point Adam.

    As for Teck Lee’s strategy, I think person #100 would be much more excited with this improved strategy: line everyone up in a circle, and have everyone do the tapping thing immediately (as opposed to before their turn). That way everyone knows what color their hat is, including fellow #100 (even though there would be no strict numbering since it’s a circle).

    Then again, if I were part of a tribe of cannibals, I would not give 99/100 of my captives the chance of escaping from the terrible of my fork. But that’s just me.

  5. how about 100/100?

    one person separates everyone into two lines- one of white only and one of black only. now 99/100 know what color is on their heads.

    then, the group that sees The Sorter’s hat is the same as theirs pulls him in. he now knows what is on his head.

    i guess it’s cheating though…

    whether it’s tapping shoulders or something like ‘shake “yes” at me if i have white on my head,’ a lot of other possible solutions are basically the above white/black sorting.

    if one wanted to do it without any “communication,” (or if you wanted a method to, as the question asks, ensure 99/100 know what color the hat is) one strategy would be tell everyone this:

    Persons 1 and 2 pair off.

    Case A: They match.

    Person 3 joins them. 1 and 2 now know they match. 3 is not sure.

    Case B: They do not match. Person 3 stands apart from them. 1 and 2 now know they do not match. They split into white and black groups. Person 3 then ‘guesses’ what he matches: 1 or 2.

    Case AA: 1, 2, and 3 match.

    Person 4 joins them. 1-3 now know they match. 4 is not sure.

    Case AB: 1 and 2 match but 3 does not.

    Person 4 does not join them. 3 now knows he does not match, forms white and black group. Person 4 then ‘guesses’ again by picking either the group with 1&2 or the group with 3.

    And so on, until the last person, who will be unsure what hat is on his head. If you want to be SURE that 99/100 survive, then some noble soul will “cross over” to the wrong group to let the final person know which is the correct group for him/her… but that’s kind of silly =P

  6. Mike says:

    Take the off and look at them.

  7. payam says:

    When the cannibal asks him what his hat’s color is, he can say “black”:

    Case A: The cannibal says “you are free”.The hat-guy remains alive.

    Case B: The cannibal says “hmm..I eat you”. The hat-guy says..”oh..sorry, I mean white”. The hat-guy remains alive.

    By my solution all the guys remain alive.