A nice puzzle for weekend :-)

[pkprasoon]

Nice puzzle

I write two different numbers, one on each hand. You choose one of my hands at random, I show you the number on that hand. You now guess whether the number you've seen is larger than the number you haven't seen. Find a strategy for guessing such that, no matter what two numbers I write, you have GREATER THAN a 50% chance of being correct

Comments

[gandalf013]

I am unable to solve this one. Not that I tried solving the problem all the time since you posted it in your blog :-). So, do you know the solution?

[pkprasoon]

No I do not know the answer. I came across this puzzle on a webiste that had no answer. :-(

[gandalf013]

Could this be as simple as “always guess that the other number is larger?”

If the numbers written belong to the set of Natural Numbers (0, 1, …), with no upper bound, then this is trivially true since given a number x in that set, and assuming that both the numbers are uniformly randomly distributed, the probability of the other number being greater than x is always 1.

Otherwise, if there is a range of numbers [0,N], then for the first number x, we say “larger” if (x+1)/(N−x) is less than 0.5.