On Thursday, January 31, 2013 12:23:35 AM UTC-8, William Elliot wrote: > On Wed, 30 Jan 2013, email@example.com wrote: > > > On Wednesday, January 30, 2013 12:29:09 AM UTC-8, William Elliot wrote: > > > > > > There is a fair coin with a different integer on each side that you can't > > > > see and you have no clue how these integers were selected. The coin is > > > > flipped and you get to see what comes up. You must guess if that was the > > > > larger of the two numbers or not. Can you do so with probability > 1/2? > > > > > > Well, there was the monty hall problem years ago. Suppose there are 3 > > > keys and you have to choose one. One of the three turns on a car's engine > > > where the other two do not. After you choose a key Monte takes one and > > > tries it in the car and it doesn't turn over the engine. He then asks > > > you if you'd like to change your mind. What should you do? You should > > > change your mind because the first key you chose had a one in three chance > > > of turning on the car where the remaining key has a two in three chance. > > > > > > Soo... > > > > > > Assuming the coin only has positive integers then you should guess > > > the number showing is the smaller integer because there are more > > > integers greater than x than there are less than x and this is true > > > for all positive integers x. > > > > > Recall, you have no clue how the integers were selected much less that > > both are positive or non-negative. > > > > Here's a variant. Instead of integers, the coin has > > a positive rational on each side.
Yeah, I was modifying the problem just slightly but as stated I agree with David Ullrich. There are just as many possitive rationals between 0 and any particular positive rational as there are greather than the particular positive rational. There is the practicality of printing any particular pair of positive rational numbers on the coin. There might be some way to take advantage of this feature just as it takes an extra character to identify a negative integer.