Trisect an Angle

Ok, here is a slightly more interesting one to further the progression of puzzles we have had here. Given a pencil and a straight edge, trisect a given (acute) angle. This is a classic geometry problem that has resisted the advances of the scale toting geometers for quite some time. Of late, a new and interesting way has been proposed to solve this problem which approaches geometry in a very nice and innovative way. I will post a hint if you guys have much trouble (though going by the other problems I have posted, this seems unlikely..)
Macaulay

A deadly gamble

You are sentenced to be hanged by the neck till death. Arnie (the governor) agrees to pardon you if you can solve this puzzle for him (since he is thickheaded as we all know). You are given a deck of 52 cards in a dark room (so you cannot see the cards). You are told from the get go that exactly 17 of these cards are face up (and the tactile feel of the cards is the same on both sides). The question then is to split the deck into two stacks which have the same number of face up cards.

- Satish

Fair toss

As you know, most coins are not perfect (i.e. the probability of heads is not equal to the probability of tails). So here is a simple probability exercise. Given a biased coin with P(heads)=p (obviously p is not a half), how would you simulate a fair coin?

-Satish

Call me!

My phone number has all the integers from 1 to 7 except one number. The missing digit is the number of times the 1's appear in the number.

The 1's always immediately follow the 2's, and are, very conveniently, equispaced.

If you remove the 1's and the 2's, the rest of the digits form a number that is a product of three prime numbers. The first prime has a single digit, the second has two digits and the third has three.

Find it!

ps: Don't friggin look at your address book...
pps: If you do figure it out, you'd better give me a holler, feller. :)

ppps: Its a US number with 10 digits.

Stability of a train

Ok, this one does not carry any points. It is only to feed your intellect; maybe even that little kid that lurks inside you and thinks about a train once in a while. With fascination and passion.

What keeps a train on the track?!