Pink Poogle Toy Forum

For some ways to think about this problem, take a peek at the discussion when Slashdot asked "How many people will choose the same option as you?". Note that the bins were much larger in Slashdot's case, so this LC will have a much different result. Also note that if you guess a large number and guess correctly, you will get a smaller reward (since you'll be splitting the pot with more people).

I think the most important insight from there is:


It's possible for there to be multiple correct answers, but I think this is rather unlikely. I would assume that they're using non-rounded percentages to determine the winner, so there's very little chance of having even one exactly-correct answer.

Update: Answer to LC 277:


And indeed, conundrum 278 is:

This is an awesome Lenny Conundrum. It is possible that there could be more than one correct answer, but if they're making us round to a whole number, then their answer must also be rounded to the nearest whole number. I'll be quite interested to see what the answer ends up being...

I made a guess towards the lower end of the spectrum; I would put my chances at about 1:20.

I guessed too high... Oh well, one more try!

One way to get a handle on the first conundrum:
1) Not everyone is going to guess reasonably. Consider how many entries are definitely going to be wrong, such as disqualifications and "100" and other random guesses near the high end. 10%? 5%? 25%?
2) Out of the remainder, assume that reasonable people will randomly guess from what they consider other reasonable people will guess. This will likely mean that guesses will be randomly distributed across the lowest X percentage points. For which Xs is it reasonable that someone might be correct? (For example, 20% would be an unreasonably high guess: even if nobody was disqualified and people uniformly guess from 1 to 20, you'd only expect 5% for each choice. In other words, there wouldn't be enough people considering 20 for 20 to be the correct answer.)
3) The largest reasonable X is an upper bound on what you should guess.

Just one pass through this logic demonstrates that the correct answer will almost certainly be less than 10%. (10%: everyone guesses uniformly from zero to ten, with no disqualifications, resulting in a winning answer of 9%.) You can then go back to step one and ask yourself the slightly more concrete question "how many will be disqualified or guess above X?" and repeat.

The second iteration of this question is going to be a bit different: more people will start guessing numbers near 3, and you have to tweak your definition of "reasonable".

(I absolutely love these questions. *grins*)