Losing to Yourself

Occasionally I play Solitaire on my iPod. After losing several games in a row (by lose, I mean I can't find anything more to do and I haven't finished the game) I wondered what percentage of games can be won and if there is any "better" methodology or rules to doing it that will yield a higher number of wins versus another.

Pure guessing leads me to believe that there are games that can't be won and that there are games that "could" be won if things are done in the right order, but can also be put into a state that you can no longer win from.

I am assuming that you are playing a "normal" game where you have 7 columns to work with (left most having one "up" card, the second having an "up" card and a "down" card ....), 4 foundation areas where you must place the cards by suit starting with Ace, and that you flip cards out of your deck 3 at a time (only able to play the top card). The version on my iPod default to NOT letting you move cards from the "foundation" areas but you could do it either way.

The puzzle I pose to everyone is to figure out what percentage of possible games are "winnable" or some approximation.

Also, can you determine any specific methodologies to increase the likely hood of winning a game over others?

Submitted by Me.

Raining goats w/ black socks

Suppose that Monty Hall (on TV's Let's Make a Deal) asks you to choose between three doors: #1, #2, and #3. Behind a random door is a new Rolls Royce. Behind each of the other two doors is a goat. Let's assume that you would prefer a Rolls Royce to a goat. You choose a door. Now, Monty, who knows which door hides the Rolls Royce, shows you a goat behind one of the two doors that you did not choose. He then gives you the opportunity to change your choice. Assume that Monty always does this, regardless of your guess. Should you change your choice?

taken from here w/ solution and some misc. explainations

There are 10 black socks and 10 white socks(no left-right distinction) in the wardrobe. Your task is to draw the minimum number of socks at random to be sure you have a pair of a single color.

How many socks should you draw?

taken from here w/ solution

The local weatherman says No Rain, and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain, and their record is 3/4.With no other data available, what is the chance of rain?

taken from here w/ solution

Ants and Nobel Prize winners Love Peanuts

On the occasion of his receiving second Nobel prize, Dr. Linus Pauling, the chemist, remarked that, while the chances of any person in the world receiving his first Nobel prize were one in several billion (the population of the world), the chances of receiving the second Nobel prize were one in several hundred (the total number of living people who had received the prize in the past) and that therefore it was less remarkable to receive one's second prize than one's first.

found here w/ solution

There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.. what is the probability that they don't collide.

randomly found w/0 solution

After a typist has written ten letters and had addressed the ten corresponding envelopes, a careless mailing clerk inserted the letters in the envelopes at random, one letter per envelope. What is the probability that exactly nine letters were inserted in the proper envelopes?

found here w/ solution

The two above puzzles w/ links should be cited as the following, per the author's website:

A. Bogomolny, Education, Mathematics, Fun, Pauling, probability from Interactive Mathematics Miscellany and Puzzleshttp://www.cut-the-knot.org/pauling.shtml#solution, Accessed 25 October 2007

A. Bogomolny, The Careless Mailing Clerk from Interactive Mathematics Miscellany and Puzzleshttp://www.cut-the-knot.org/Probability/TenLetters.shtml, Accessed 25 October 2007