Happy New Year!!!
Sorry I am a bit lazy, but it is a holiday season!
Lets end this year with a Nim game.
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.