RIDDLES

SYMBOLS
M Needs math past arithmetic and basic probability.
C Requires knowing how to play chess.
P Physics knowledge is helpful.
>=P I don't know the solution to this problem myself.
CPU Requires calculator/computer power.


FORUM
1-GLOBE TRAVERSAL

how many places are there on the earth that one could walk one mile south, then one mile west, then one mile north and end up in the same spot? to be precise, let's assume the earth is a solid smooth sphere, so oceans and mountains and other such things do not exist. you can start at any point on the sphere. also, the rotation of the earth has nothing to do with the solution; you can assume you're walking on a static sphere if that makes the problem less complicated to you.

Hint 1: think you've figured it out? do you know that there's more than one? in fact, there are more than two. also note that walking north from the north pole (or south from the south pole) is illogical and therefore does not enter into the problem. all normal assumptions about directions will be used.

Hint 2: christopher columbus.
2-GHETTO ENCRYPTION I

You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route. How can you send the object securely?

Alternative, more precise phrasing: Andy and Grant are staying in different rooms in the same hotel. Andy needs to give a gold pendant to Grant, but spies are trying to assassinate Andy and Grant so neither of them can leave their room. The only way they can transfer objects is by using the bellhops. Both Andy and Grant have a safe with a large clasp that can be secured with a padlock. Both Andy and Grant have a padlock and a corresponding key. (So 1 gold pendant, 2 safes, 2 padlocks, and 2 keys.) But the bellhops are thieves. Anything that is not padlocked in the safe will be stolen by the bellhops - including any unlocked padlocks, the keys or the pendant. How can Andy transfer the gold pendant to Grant without it being stolen? (where both sides have encryption capability, and where unsecured items are taken away rather than just copied?)
3-GHETTO ENCRYPTION II

Three coworkers would like to know their average salary. However, they are self-conscious and don't want to tell each other their own salaries, for fear of either being ridiculed or getting their houses robbed. How can they find their average salary, without disclosing their own salaries?
ADJACENCY GRID

arrange the numbers 1 to 8 in the grid below such that adjacent numbers are not in adjacent boxes (horizontally, vertically, or diagonally).
1
6 4 3
2 7 5
8

the arrangement above, for example, is wrong because 3 and 4, 4 and 5, 6 and 7, and 7 and 8 are adjacent.
4-FAUSTIAN ROUND TABLE COIN GAME

you die and the devil says he'll let you go to heaven if you beat him in a game. the devil sits you down at a round table. he gives himself and you a huge pile of quarters. he says "ok, we'll take turns putting quarters down, no overlapping allowed, and the quarters must rest on the table surface. the first guy who can't put a quarter down loses." you guys are about to start playing, and the devil says that he'll go first. however, at this point you immediately interject, and ask if you can go first instead. you make this interjection because you are very smart, and you know that if you go first, you can guarantee victory. explain how you can guarantee victory.
5-DOMINOES ON A CHESSBOARD

using 31 dominoes, where one domino covers exactly two squares, can you cover all the empty squares on this chessboard (which has only 62 spaces, since two opposite corner squares are removed). if so, how? if not, why? prove your claim.
MANHOLES.