## Hard!!!!!

i cant seem to be able to beat this guy...and to tell u thr truth, i feel like going in my computer screen and punching him in the face, lets see if any of u can get this , cause i certainly cant

http://www.ebaumsworld.com/pearl.shtml
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 Recognitions: Homework Help Science Advisor There are a couple ways of beating him. You can figure it out on your own if you use some brute force, listing out a bunch of the possibilities at a given stage, and some logic, eliminating some of the many possibilities. Start from the final desired state, and work your way backwards. After going down the "tree" 4 or 5 levels, you'll have a lot of different possibilities to work with, but by then you should be able to see what works and what doesn't. That was my way, there's a nicer, neater, more general way to solve this, and here it goes: Write the number of pearls in each line in binary, so starting with 3, 4, 5, 6, you have: 0011 0100 0101 0110 Now, add each column up, one column at a time, modulo 2. In other words, at the bottom of each column, write a 1 if there are an odd number of 1s in the column above, and a 0 if there are an even number, like so: 0011 0100 0101 0110 ----- 0100 Now, whenever it's your turn, your goal is to always have that "sum" (like 0100 in this case) to be all zeroes. If you remove 4 pearls from the row of 4, 5, or 6, you'll get: 0011 0000 0101 0110 OR 0011 0100 0001 0110 OR 0011 0100 0101 0010 However! This only takes you so far. Once the number of pearls gets small, this approach breaks down. Imagine you've left it with 2 rows, each containing 1: 0000 0000 0001 0001 ---- 0000 Looks good, right? Wrong. Obviously, that guy will just take 1, leaving you with 1 and you lose.
 I hate playing games like that, especially with a computer, because there's probably some algorithm that makes winning trivial for those who know (or who are programmed with) the trick.

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