Ask HN: What are your favorite brain teasers?

6 points

17 years ago

The other day I encountered an interesting problem: You have two fair, six-sided die with positive-integer-valued faces. You roll the die, and take the sum S of the numbers you roll. S will have some frequency distribution. For standard die, theres 1 way to roll a 2, 2 ways to roll a 3, etc. Are there any other pairs of die (the dice need not be identical) that generate this same frequency distribution?

It turns out this problem has a unique solution, and a nice name: http://en.wikipedia.org/wiki/Sicherman_dice

I encounter pretty cool problems like this on a regular basis, but they are always by way of a random friend or blog post - there doesn't seem to be a good central resource for such things. This may be because any problem that enough people know about is no longer novel or interesting (think of all the tired brainteasers you know of).

Nonetheless, I'd be interested to hear of other peoples' fun brain teasers. What are some of your favorites?

4 comments