This cool puzzle (and solution) comes from my friend Mike.

Alice secretly picks two different real numbers by an unknown process and puts them in two (abstract) envelopes. Bob chooses one of the two envelopes randomly (with a fair coin toss), and shows you the number in that envelope. You must now guess whether the number in the other, closed envelope is larger or smaller than the one you’ve seen.

Is there a strategy which gives you a better than 50% chance of guessing correctly, no matter what procedure Alice used to pick her numbers?

I initially thought there wasn’t, or that the problem was paradoxically defined, but it turns out that it’s perfectly valid and the answer is “Yes.” See my first comment for an example of one such winning strategy.

*This puzzle is similar to, but not the same as, the **two envelopes paradox**. For more time-devouring reading, see Wikipedia’s **List of Paradoxes**.*

### Like this:

Like Loading...

*Related*

Your way to enlighten everything on this blog is actually pleasant, everyone manage to efficiently be familiar with it, Thanks a great deal.

LikeLike

Il tuo modo di illuminare tutto su questo blog è davvero piacevole, tutti riescono ad essere efficacemente familiarità con essa, ringraziamenti molto.

LikeLike

There is of course, a really simple method of finding the answer, and that is through the amazing power of liberal arts, namely linguistics.

The question is whether we can guess with more than 50% accuracy whether the number we chose is “smaller or larger”.

It was also two different reals, so they cannot be the same.

Therefore with 100% accuracy, we can say that yes, this number is smaller or larger than the other number, which is what the riddle asked about.

LikeLike

Very helpful information.

LikeLike

Excellent information on your blog, thank you for taking the time to share with us.

LikeLike

I will recommend reading it to all my friends!

LikeLike

I would really appreciate the efforts you all have made here to make this page more informative.

LikeLike

I really enjoy simply reading all of your weblogs.

LikeLike

Very cool selection of furniture, I like very much!

LikeLike

Very helpful information.

LikeLike

Thanks for posting this info. I just want to let you know that I just check out your site and I find it very interesting and informative.

LikeLike