General Forums > Academic / School

The Puzzle Thread!

(1/4) > >>

Sidoh:
Lots of smart people here.  This calls for a puzzles thread.  I've heard a few new (and old) ones recently, and thought I'd share.  Here's how I'm gonna run it:

1. All puzzles will be listed in this post.  I'll edit the post to add new ones.  Add a post/send a PM and I'll add yours to this post.
2. PM answers, add posts to ask questions.
3. I'll indicate who has solved each of the puzzles underneath it.

Let's do this.


--- Quote ---You gather 100 perfect logicians. You tell all of them the following:

* They will be placed in a room with 99 other perfect logicians, in a circle so they can all see eachother
* Their head will be painted a particular color; they cannot see the color of their own head, but everyone else can
* At least one of the hundred's head's will be painted blue
* You will flip the lights on and off
* If they figure out their head is painted blue, they must leave next time the lights go off
* They are not allowed to talk or signal each other in any way. They may only observe the others, and leave if/when they figure out their head is blue.
You proceed to paint all of their heads blue, and begin the exercise. What happens, if anything, and when?
--- End quote ---


--- Quote ---Prove or disprove: you can completely fill a cube with finitely many smaller, all-differently-sized cubes.
--- End quote ---


--- Quote ---You have 100 pennies.  Exactly 50 of them a heads-up, but you don't know which ones.  If you're blindfolded, how would you divide the pennies up into two groups with an equal number of heads?  Repeat the same exercise when exactly 10 of them are heads-up.  You're not allowed to feel the pennies to test if they're heads up.  Say you're only allowed to touch the pennies by gripping them on the edges.
--- End quote ---
SOLVED BY: dark_drake


--- Quote from: nslay on March 18, 2011, 12:51:49 am ---I came across this problem recently

Given [latex]\{ f_m(\mathbf{x}) \}_{m=1}^M,\ f_m(\mathbf{x})\ :\ X \subseteq \mathbb{R}^n \to \mathbb{R}[/latex] and denote
[latex]
\mathbf{f}(\mathbf{x}) = \begin{bmatrix} f_1(\mathbf{x}) & f_2(\mathbf{x}) & ... & f_M(\mathbf{x}) \end{bmatrix}^T
[/latex]

Under what assumptions is the matrix
[latex]
H = \int_X \mathbf{f}(\mathbf{x}) \mathbf{f}(\mathbf{x})^T d \mathbf{x}
[/latex]
strictly positive definite? Here integration is component-wise.

--- End quote ---

dark_drake:
Why would perfect logicians hang out in a room with heads painted blue?

Sidoh:

--- Quote from: dark_drake on March 17, 2011, 09:37:52 pm ---Why would perfect logicians hang out in a room with heads painted blue?

--- End quote ---

All perfect logicians hang out in a room with their heads painted blue (or red).

deadly7:
So Blue Man Group is perfect logicians?

Sidoh:

--- Quote from: deadly7 on March 17, 2011, 11:33:28 pm ---So Blue Man Group is perfect logicians?

--- End quote ---

No, no.  The converse is not true.

Navigation

[0] Message Index

[#] Next page