Math Puzzle Thread

[ZEE]

YAY!

[LordShiva]

Here we go: every prisoner sums all the other prisoners colours (assign each colour a number from 0 to n-1), takes modulo n, and adds i-1, where i is his place in the line.

edit: Kuci beat me to it.

[Kuciwalker]

I'm going to poach some from my CS homework. This was an easy one (we had to prove it, but the proof is trivial once you know the answer):

After a long day of 251 homework, you and your friend decide to treat yourself to a circular 12-cut
pepperoni pizza. When the pizza gets to your place, Vocelli’s makes dividing the pizza hard on you, by
putting a different number of pieces of pepperoni on each slice. You and your friend decide to divide
the pizza in the following way. First, you choose and eat any slice from the pizza. Then, you both
alternate turns by taking and eating a slice from the pizza, but only one of the slices that borders the
gap left by the removed slices.

Is there a strategy you can use to ensure that you will have eaten at least as many pieces of pepperoni
as your friend, once the pizza is fully consumed?

[b etor]

251 homework? what's that?

yes. steal your friend's pepperoni when s/he is not looking.

[Kuciwalker]

251 is the course number.

[b etor]

oh.

[Kuciwalker]

Oh come on people, the answer is trivial.

[Main_Brain]

Peperoni Pizza Questions make me hungry.

Use Nash Bargaining Solution

[SlowwHand]

I think math freaks should be rounded up and shot .

[Kuciwalker]

You misspelled "Texans" and "the French" - not that there's a difference.

[b etor]

for the pizza, take the piece iwth the most pepperoni. your friend will probably do the same. then from the available pieces take the one with the most amount of pepperoni.

or you could eat with a vegetarian.

[ZEE]

Originally posted by SlowwHand
I think math freaks should be rounded up and shot .

[Kuciwalker]

Originally posted by b etor
for the pizza, take the piece iwth the most pepperoni. your friend will probably do the same. then from the available pieces take the one with the most amount of pepperoni.

That doesn't guarantee you'll have at least as many pepperonis.

[b etor]

if your friend were a vegetarian it would.

[Lul Thyme]

Re: Math Puzzle Thread

Originally posted by Ramo
I heard a neat one recently.

There are N people in a dungeon. The dungeon master has a a bunch of colored hats, with an arbitrary distribution among N distinct colors (they could all be blue, there could be one of each, etc.). He tells them that he's going to distribute the hats to everyone, and at least one person has to guess his or her hat correctly or else everyone dies. He allows them to meet and discuss some sort of algorithm to figure out how to do this in advance. After he distributes the hats, they aren't allowed to communicate, signal, etc. in any way. All they can do is see the color of everyone else's hat.

So what strategy should they take? You can suppose that everyone has a really good memory.

That's a very nice one.
Was asked at last
Christmas party here.
Took me about 10 minutes.


To answer a lot of Kuci's question :
-the list of N colors is known in advance
-they can discuss as much as they want beforehand
-when they are ready, they are sent to different cells, and are sent a list of the colors of the other person.
-each person takes one guess
-if at least one person guesses right, they all win.

This removes all problems of timing and communication.