The online computer game is interesting, but takes too much time.

I was a fan of SOKOBAN, too. When my father visited me couple years ago. He was deeply into it as well. During the time of his stay, we finished all 99 (or 100?) levels. He even wrote down all the solutions.

Before I post my solution, Mr.Puzzle, can you post your answer to the ants problem?

Here's my solution of this week's M&M problem:

We have to think "When will I lose?" if I have this many M&Ms to start with. Here are the numbers:

2: I can't take all of them. I can only pick one, and the opponent pick the last one. I lose.

3: If I pick one, the opponent picks 2, and vise versa. I lose.

4: I WIN. I pick one and leave the opponent 3, then see above.

5: I lose. If I pick one, that leave the opponent 4, a winning number. If I pick two, the opponent takes the rest 3.

6,7: I WIN. I leave opponent 5 by picking one or two.

8: I lose. If I pick 3 or more, he takes all. Else, he leaves me 5, a losing number.

9,10,11: I WIN, I can leave him 8.

12: I lose. If I pick 4 or more, he takes all. Else, he leaves me 8, a losing number.

.... and on and on.....

So the losing numbers are: 2, 3, 5, 8, 12, 18, 27, 41, 62, 93, ....

or A<n> = ceiling of A<n-1> * 1.5

Besides these starting numbers, I can win by taking down the numbers to the previous "losing number". Then the opponent will neither be able to take all of the rest to win, nor can he take the number down to another "losing number".

Right, Prof.10K? I will post another M&M problem after I see your answer.