c4countdown

So I came up with this puzzle myself on the train earlier (admittedly I’m sure there’s many similar out there). I don’t know the answer myself (or even if there is an exact answer) and advanced apologies if I explain this really shittly.

Say 20 people are stood in a line and somebody comes along and says ‘I’m thinking of an integer between 1 and 20 and I’ll give the first person that guesses it £1000’.

So people go down the line taking it in turns to guess, but as soon as the correct answer is guessed the game is over, so if the first person guesses correctly its tough luck for the other 19 they don’t get a guess. Each player only gets one each guess and the remaining players are allowed to hear (and even write down) the incorrect guesses.

Now say you were involved in this game and you and only you were given special dispensation to choose your place in the line; is there a definite answer as to which would be the best place to be stood in the line and if so what would it be?

I'm probably completely wrong, but I think they're all equal.

Your chance of getting it right is 1/q , where q it the amount of people left including you (21-your place).
This should be multiplied by the chance of someone else having not already guessed it, so q/20 .

You then get 1/q*q/20 , which cancels to 1/20 .

QED.

You should go first because you'll kick yourself if somebody says the number you were thinking of and gets it right.

I agree with Thomas, your chance of victory is 1/20 no matter where you stand in the line.

I agree with Nick. The Task Force lyric "[it's] like being sixth place in a game of Russian roulette" always annoyed me because sixth place is no better or worse than anywhere else. (I know what he meant to say but come on Chester, you're supposed to be a professional.)

Charlie Reams wrote:I agree with Nick. The Task Force lyric "[it's] like being sixth place in a game of Russian roulette" always annoyed me because sixth place is no better or worse than anywhere else. (I know what he meant to say but come on Chester, you're supposed to be a professional.)

If you're talking about a game of Russian Roulette where you each have to take a barrel which hasn't been picked yet, then sixth would be slightly different in that you'd know you were going shoot yourself if you went last if there were 6 chambers and nobody else had been shot. But nobody I knows plays Russian Roulette like that anyway, when my mates & I play, we always just have a completely free spin of the barrel. At least we used to, before they all died.

Jon Corby wrote:

Charlie Reams wrote:I agree with Nick. The Task Force lyric "[it's] like being sixth place in a game of Russian roulette" always annoyed me because sixth place is no better or worse than anywhere else. (I know what he meant to say but come on Chester, you're supposed to be a professional.)

If you're talking about a game of Russian Roulette where you each have to take a barrel which hasn't been picked yet, then sixth would be slightly different in that you'd know you were going shoot yourself if you went last if there were 6 chambers and nobody else had been shot.

Yeah, that's what I was addressing in the parenthesis. He ought to say "given that the previous five were okay", or perhaps deploy some sort of probabilistic notation.

It's a constant wonder how you didn't turn out to be a rapper, Charlie.

Surely the best place to be is when there are 2 options left? If someone goes first they have a 1/20 chance of guessing the number - extremely unlikely. If you were second in line you'd have 19 to choose from which is better but still unlikely to win. Continue this down to 3 numbers left. The chance of picking the right number is 1/3 so I'd rather be the 2/3 dude....then when it's down to 2 you have a 50/50 chance of winning. Isn't it like the Monty Hall problem?

Kirk Bevins wrote:Surely the best place to be is when there are 2 options left? If someone goes first they have a 1/20 chance of guessing the number - extremely unlikely. If you were second in line you'd have 19 to choose from which is better but still unlikely to win. Continue this down to 3 numbers left. The chance of picking the right number is 1/3 so I'd rather be the 2/3 dude....then when it's down to 2 you have a 50/50 chance of winning. Isn't it like the Monty Hall problem?

In fact, you should definitely go last, because then you're guaranteed to win.

By your (flawed) reasoning, wouldn't being last and having a 1/1 chance be best?