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The One Hundred Challenge

You're probably wondering how the computer can almost always force a win. The method is simple.

Before we begin, we must discuss the number eleven. If I want to reach a specific total, then on my turn, all I have to do is set the total to eleven minus that number. Why? Because you must add no less than one point and no more than ten points to the total. This means that the maximum amount that can be added to the total before it gets back to my turn is eleven. For example, if I wanted to reach 44, on my turn I would try to get the total to 33. If you added even a single point to this total (making it 34), I would add ten and get 44. If you added 10 points (making it 43), I'd add 1. In fact, if you added N points, on my turn I would add (11 - N) points.

How is this useful? Using the above logic, if I can set the total to eleven points below my target and force you to take a turn, I can reach the target. The target for the game is 100 points. Therefore, I want the total to be 89 (100 - 11 = 89). So, if you let me get the total to 89, I win.

But let's be a bit shrewd here. Suppose that I want the total to be 89. I could force you to let me get 89 if the total after my last turn was 78. And I could get 78 if I had it at 67. In short, as soon as I can get to any of these totals:

provided that every move takes me to the next total, I have a mathematically forced victory.

Now that I've shown you my secret, I will expose the only way to beat me. Look at the first total on the list (1). You have the first move. If you on your first turn add 1 to the total, and then, from every point on, add eleven minus my last addition, you cannot lose. But be careful, if you make a mistake, I have no reservations against stealing the victory for myself!