Warm-Up 4, Due Thursday, February 14, before noon.

Warm-up questions usually either address material we handled during last class, or material you were to read in preparation for class, or you are supposed to answer questions based on your common sense alone. Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try to tell me why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

Your Name:

Do you know how to play checkers? If not, learn it in 3 minutes here.

Then please read this (very short) NY Times article, and answer the following questions:.

Question 1

Can you describe the conclusion of the article? What does Jonathan Schaeffer claim, and what has it to do with draws?

Question 2

The article claims that in chess there are "between 1040 and 1050 possible arrangements of pieces", far more than checkers which has "5 * 1020 positions". Does this make sense to you? If not, how many possible arrangements of pieces do you estimate chess has? What about checkers? How many positions do you estimate checkers has?

Question 3

Play ten rounds of the game NIM(7) (with 7 stones) against the computer on this webpage. The rules of the game explained there. The computer plays very sophisticated, but you should still be able to win. Explain how to win this game against the computer.

Question 4

What about NIM(9) (with 9 stones) on the same webpage. Can you still win? Even once? Can you explain why and how the computer always wins?