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Today's Puzzle a.k.a. Stupid S4 Tricks
23rd-Nov-2006 11:59 pm
You have one (1) ordinary six-sided die (i.e., the traditionally marked, uniform-density, cubical kind that you could find in any Vegas casino within about 5 minutes).

You need to make a random choice between four (4) alternatives, same probability for each (25%, i.e., barring the occasional coin-landing-on-edge weirdness that supposedly can happen in real life, which we won't worry about).

You could, e.g., roll the die and if you don't get 1,2,3,or 4, just roll again and keep rolling until you do. That would be too easy, and also could conceivably take a while if you get unlucky with the 5s and 6s.

But the real problem is that, due to various contrivances entirely beyond your control, it just so happens that if you roll the die a second time, you will be plagued by frogs, and (trust me on this) you really do not want to be plagued by frogs.

So you absolutely have to do it in one (1) roll. Good luck.

Well okay, if that one was too hard, here's an easier one:
You're running a meeting and there are four people who want to speak. You need to randomly decide what order they go in and you want to be Completely and Utterly Fair about it ... meaning each of the (4!=24) possible permutations of the speakers has to be equally likely. Once again, you have one (1) six-sided die, and the frogs will only allow it to be rolled once. Good luck.

24th-Nov-2006 03:16 pm (UTC)
Orientation of landing die on 3 and 6 for the first one (or 5 and 6, but you don't have to look at the sides if you pick 3 and 6), top and number facing a specific side of the table surface yields all 24 possibilities for the second. That seems kind of hacky, but I can't think of another answer that doesn't involve things like very specific timing or number of bounces or other things that can't be made particularly random without extra data not given here.
24th-Nov-2006 04:51 pm (UTC) - Solution ..
Assign everyone two corners of the die, roll it and push it into a corner. Whoever gets their corner into the corner wins. yay.

And having done that, you can see that 24 = 8 corners * 3 orientations. So same kind of thing -- when you push a d6 into a corner it can have any of 24 orientations ..
24th-Nov-2006 06:24 pm (UTC)
Some "lateral thinking" solutions...

Divide the table into four quadrants, drop the die onto the middle point, and see which quadrant it lands in. Or just divide it into halves and use the parity of the number rolled (odd or even).

Stick pushpins into opposite sides of the die (or otherwise attach something) so that only the remaining four faces can be landed on.

Trade it to someone who has a four-sided die. (This is the "give the barometer to the superintendent" method.)
25th-Nov-2006 04:54 am (UTC)
Luckily, the frogs are somewhat less cranky than usual, today.