What is the smallest NxN box ?

]]>Which way was I facing after I did that forever?

]]>Two needles achieve nothing beyond a small dose of pain. One can be found on the left side of the one you seek. The other lies to the left of an interesting little creation.

Your own past is often your worst enemy. Here you have a chance to relive it. The first and last needle each have not what you seek but while one contains illness and pain…the other provides release.

Sleep lies to the right of death and to the left of nothingness.

The one you seek shall lie between blissful nothing and quiet repose. Be warned…the price for failure is high.

]]>I’ll bring you (but not your buddy yet) into a room where I have a bunch of coins lined up in a row, probably randomly distributed between being heads up and tails up, and I’ll tell you which coin among those is the bazillion dollar coin. Then you’ll exit the room and your buddy will come in through another entrance (so you can’t communicate after I tell you which is the bazillion dollar coin) and tell me which coin to give to the two of you.

That wouldn't be a very fair game, so you can also tell me to flip whichever coins you want before you leave the room and your buddy comes in. (I’m flipping them myself to make sure you don’t send codes with subtle placement of the coins or such tomfoolery.) But you have to watch 10 minutes of Nyan Cat for every coin I flip so you want to minimize the number of flips lest you go insane. I’m not saying beforehand how many coins will be in the room, and you only get one minute to tell your buddy a strategy (just words that can be spoken in under a minute, no written cheat sheets) before it’s time to play the game.

Clock starts now.

(I would credit the source of where I heard the original form of this puzzle that I'm modifying, but I can't remember the source any more.)

]]>What are the chances of no encounter if there are …

(b) Four ants, each placed on the vertices of a tetrahedron?

(c) Eight ants, starting at the corners of a cube?

]]>He then inexplicably states that, even though you might disagree, the correct answer is actually 5!

Explanation?

]]>Explanation?

]]>What is the probability that Al must move?

]]>Here we seek the shortest set of line segments, one attached to each of a square's corners, that need not connect with each other. Instead, what we ask of the line segments is that is they will block any ray of light attempting to pass through the square.

]]>The bad news: I do not know the solution and I cannot ask for hints.

]]>
*a ^{b}* x

You have been chosen as the Royal Advisor to the Princess and tasked with implementing her best strategy to choose the Most Wonderful Prince of the realm. You devise an evaluation scheme by which the princess can assign a unique "wonder number" to each prince as she meets him. The strategy then is to have the Princess reject, but record the highest score of, the first N princes that she meets. The Princess will then choose the first Prince that she subsequently interviews whose score exceeds that recorded score.

That's it. The puzzle is basically solved. Except, of course, to decide on the optimal value of N. It requires some thought. If N to too high, the most wonderful prince is likely to be eliminated at the outset, and she ends up with the last guy. If N is too small, the Princess will likely settle for a fairly undistinguished prince.

What value of N optimally balances these two risks? What is the probability that the Most Wonderful Prince will be chosen?

Disclaimer: I recall this puzzle being posted before, with different flavor text. And it's somewhat of a classic. To give it a fair play here, I'll ask not to post any links and not to just give the answer if you know it, at least not without "showing your work."

]]>If there were 6 cabins in all, how might they be placed, so that using Al's nearest-neighbor algorithm, and selecting the worst initial cabin, Al would be forced to walk the greatest distance; and what is that distance?

Examples:

2 cabins: diagonal corners, starting at either: 2 x sqrt(2) = 2.828... miles.

3 cabins: any three corners, starting at any of them: 2 + sqrt(2) = 3.414... miles.

Check out n=4 and n=5 as a warm-up.

]]>

x^(x/2)^(x/4)^(x/8)^(x/16)^(x/32)....

(a) as x goes to infinity

(b) as x goes to zero

]]>
today I found myself in front of the following codified text:

MzIgVCA2NTg3MjYgNDg1MTY0Nw0KMzIgVCA2NTc5OTkgNDg1MzExMw0K__MzIgVCA2NTc0MDUgNDg1MjMxM A0KMzIgVCA2NTg2MzkgNDg1MTgzMg0KMzIgVCA2NTc1NDIgNDg1MzY4NA__0KMzIgVCA2NTgwMTMgNDg1MTQ 0Nw0KMzIgVCA2NTc3MzMgNDg1MzMxNQ0KMzIgVCA2NTcyMjggNDg1MzM0Mw0KMzIgVCA2NTc4NDggNDg1 MTY3OA==

`I know that the text is composed of geographic coordinates.`

and that the text: "MzIgVCA2NTc0MDUgNDg1MjMxM A0KMzIgVCA2NTg2MzkgNDg1MTgzMg0KMzIgVCA2NTc1NDIgNDg1MzY4NA"

corresponds to the coordinates:

- 32 T 657405 4852310
- 32 T 658639 4851832
- 32 T 657542 4853684

MzIgVCA2 NT c0MDU gND g1M jMxMA 0K -> 32 T 657405 4852310

MzIgVCA2 NT g2Mzk gND g1M TgzMg 0K -> 32 T 658639 4851832

MzIgVCA2 NT c1NDI gND g1M zY4NA 0K -> 32 T 657542 4853684

what is the encryption key?

]]>1. Brown and Smith each won $10 playing poker with the pitcher.

2. Hunter is taller than Knight, and shorter than White, but each weighs more that the first baseman.

3. The third baseman lives across the corridor from Jones in the same apartment house.

4. Miller and the oufielders play bridge in their spare time.

5. White, Miller, Brown the right fielder and center fielder are bacheloros. The rest are married.

6. Of Adams and Knight one plays an outfield position.

7. The right fielder is shorter than the center fielder.

8/ The third baseman is a brother of the pitcher's wife.

9. Green is taller than the infielders and the battery (the pitcher and the catcher), except for Jones, Smith and Adams

10. The second baseman beat Jones, Brown, Hunter, and the catcher at cards.

11. The third baseman, the shortstop and Hunter made $150 each speculating in General Motors stock.

12. The second baseman is engaged to Miller's sister.

13. Adams lives in the same house as his sister but dislikes the catcher.

14. Adams, Brown and the shortstop lost $200 each speculating on wheat futures.

15. The catcher has three daughters, the third baseman has two sons, but Green is being sued for divorce.

]]>
* Edit*: Ignore the original text in pink. Instead,

What is the distance to the origin of the centroid of the possible termination points? You find the centroid of a set of points by averaging respectively their *x- *and *y- *coordinates.

First correct answer wins, but style points will be awarded as well.

]]>Can you find a way to overlap circle A with portions of some or all of the other four circles so that the un-overlapped portion of A has the same area as the sum of the unoverlapped portions of the other four circles? That is, the red area is equal to the sum of the green areas. Circles B, C, D and E may overlap portions of each other as well as a portion of A.

]]>

Cmon try to solve

]]>This is a Gold star puzzle.

]]>