Wednesday, January 6, 2010

Thought Process during the Tiger's Number Guessing Game

The following may be cryptic but it was our thought processes when we played the tiger's number guessing game. We're sure that in the future, we'll forget about it, hence we're recording it such that we may look back on it with nostalgia.

During our time playing the number guessing game, our best record was winning on round 2 (which was quite scary due to the bug of winning on round 1) while the worst was winning on round 8 (which usually left us frustrated as it meant that we overlooked something). Most of the time, we would win on round 6 which at tier 2, would give us 5 points. Reviewing the rules of the game, the tiger is thinking of a 3 digit number consisting of the digits 0 through 9. We must enter a 3 digit number otherwise a chance to guess is wasted as the guess is counted as incorrect. For a given 3 digit guess, if a digit is present and in the correct position of the 3 digit number, the tiger will move its front paw. If a digit is present but in the wrong position, the tiger will move its rear paw. There isn't a need to stare at the tiger for paw movement as someone else will notice it and announce it.

So within the first 3 rounds, we try to gather all the clues necessary to determine the location of the 3 digits. We do this by guessing 3 sets of numbers: 135, 246, and 789. The actual digits didn't matter so long as they don't repeat and 0 is not part of them. In quite a few of the cases, just guessing 135 and 246 was enough to determine that all 3 digits was a part of those 2 sets of numbers and which set contained more digits than the other.
The best possible outcome other than guessing correctly through luck is to have a guess show that all 3 digits are part of the same set. At this point, the correct number can usually be determined in 2 guesses, if not the very next guess. This is because all that is required is to swap or shift digits.

The next best outcome is if it is shown that the digit 0 is present. The digit 0 is present when guessing the initial 3 sets only shows the presence of 2 digits. We intentionally left out guessing 0 as part of the initial 3 guesses because the digit 0 can only appear in the 2nd or 3rd positions so it was a waste to leave out what we could determine from the 1st position. If the digit 0 is present, always include it in the future guesses and note whether we have it in the correct position. This reduces the number of digits and positions that we have to determine down to 2.

The next desirable outcome is to have 1 set contain 2 digits. Although we don't know which of the digits are the correct ones, we can usually determine from the next guess whether we've excluded the correct one. If 1 or more of those digits are already in the correct positions, it's even better.

The worst outcome is to have each of the 3 initial sets contain 1 correct digit each and in the wrong positions. In that case, the 4th guess will contain a digit from each of the 3 initial guesses but at different positions than they appeared in the initial 3 guesses. Then the 5th guess will contain 2 of the digits from the 4th guess but a different 3rd digit and at a different position while still keeping the rule of having 1 digit from each of the 3 initial sets. Regardless of how the tiger move its paws, we would have definitely determined one of the digits on that 5th guess, and hopefully in the correct position too.

So in summary, we try to have each guess reveal as much information as to the presence of digits and their positions as possible. Unless we are absolutely certain about whether a digit is present and at the correct position (which we can usually only do with the digit 0), we move each of the digits to different positions. By the 5th guess, we can then use the process of elimination and what-if scenarios to determine the correct answer at the 6th guess.

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