Problem 44630. Guess the number I'm thinking of (Part 1)
 I randomly choose an integer between one and ten (inclusive). I don't provide any clues about the number.
 Your first opponent tries to guess the number. They guess randomly.
 Your second opponent tries to guess the number. They also guess randomly.
 You try to guess the number. But you guess strategically.
 The winner is the person who guesses my chosen number, or the person who guesses closest to my chosen number. This represents a "win".
 If two contestants are equally close, they may share the win, with such a result being declared a "draw". (It is a loss for the remaining contestant.) A draw is worth half as much as a win.
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In some cases, it would be strategically beneficial to guess the same number as one of your opponents. For example, if they guess 7 and 9, for example, you would generally earn more points guessing 7 than any other number, as you would earn an extra half point from the draw if the number is 7 or 8 (which is a threeway draw) and not lose any of the full points if the number is 16.
Hi, James. That may be a valid point ...when playing with different rules. I deliberately set the constraint that all three guesses (from the three contestants) must be different. If my constraint were removed, then you would have freedom to implement that strategy; it would also mean you'd have to handle the situation of your opponents choosing the same number. However, I personally would not be scoring a threeway draw the same as a twoway draw. Consider if each person pays $1 into a 'prize pool' to enter: if you achieve a twoway draw, then you get back $1.50 (a 50¢ profit); but in a threeway draw nobody would get any profit, and hence I would be scoring it as if that 'game' never happened. —DIV
Understood, and I agree that a threeway draw (not possible with the current rule set) should definitely be scored differently than a twoway draw.
My code worked, although not quite as well as Tim's. I'll have to check the algorithms he used to generate his solution, and see how it differs from mine.
I figured out why Tim's solution scored higher than mine. My code gave me half credit for a few oddball cases where there was a tie between two of us but the third person was closer to the correct number. It didn't happen enough for the solution to fail the tests, but it was still suboptimal.
This is a great problem. I was planning to eventually do one like this, but now I don't have to, as this one is very well implemented.
By the way, more problems like this one would be great, too.
Thanks. There are indeed some more that I have thought of like this....
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