Monday, December 31, 2012

Happy New Year!!!

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Happy New Year!!!


Sorry I am a bit lazy, but it is a holiday season!

Lets end this year with a Nim game.

2013=(11111011101)
Lets play a Nim game with three heaps:

*****
***
*


Who will be the winner?

First heap's nimber is 5=(101),
second heap's nimber is 3=(011),
last heap's nimber is 1=(001).
So the nim sum is (101)+(011)+(001)=(111) which is nonzero. Therefore the first player has a winning strategy.

(111)+(101)=(010)=2, so the first player takes 3 and leaves 2 in the first heap.

Lets talk about binary numbers in the next blog.