Forum:

Programming Diversions

Unanswerable puzzle?

Junilu Lacar

Sheriff

Posts: 17652

300

I like...

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

~~Given the following choices, what's the probability of randomly choosing one and being correct?~~

What is the probability of randomly picking the correct answer to this question?
1. 25%
2. 0%
3. 25%
4. 50%

[Question edited for brevity]

Piet Souris

Bartender

Posts: 5475

212

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

At this site, we usually respond with: what do YOU think, and we'll let you know what we think

There are three kinds of actuaries: those who can count, and those who can't.

Campbell Ritchie

Marshal

Posts: 79422

377

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

That puzzle belongs in MD! It has four answers, all of them wrong

Stephan van Hulst

Saloon Keeper

Posts: 15621

366

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

That's not true Campbell. If all answers were wrong, then answer 2 would be correct. Instead, the problem is undecidable, or rather, the question is unanswerable.

The issue is that the question is self-referential. It falls square in the same domain as Russell's Paradox. I think Gödel would say that you can't at the same time pose or understand the question, and give a correct answer to it in the same terms used by the question.

Junilu Lacar

Sheriff

Posts: 17652

300

I like...

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

Stephan van Hulst wrote:The issue is that the question is self-referential. It falls square in the same domain as Russell's Paradox. I think Gödel would say that you can't at the same time pose or understand the question, and give a correct answer to it in the same terms used by the question.

Hammer meets nail right on the head.

Junilu Lacar

Sheriff

Posts: 17652

300

I like...

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

Stephan van Hulst wrote:If all answers were wrong, then answer 2 would be correct.

This is the paradox because if answer 2 is correct then clearly not all the answers are wrong. It's the Schrodinger's cat answer.

Piet Souris

Bartender

Posts: 5475

212

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

The question is meaningless. What is the answer to the question: is 25% correct or not? But the fun is of course that if 0% is correct (??) then we have 25% chance of getting it right. So with 50% chance we get it right. But choosing 50% has only 25% chance, ad infinitum.

Wasn't it Hilbert cs who tried to tame self-references?

There are three kinds of actuaries: those who can count, and those who can't.

Stephan van Hulst

Saloon Keeper

Posts: 15621

366

posted 9 months ago

Number of slices to send:

Optional 'thank-you' note:

Send

Pretty much any mathematician worth their salt was at it at that time, seeing as that set theory was being recognized as bedrock upon which all mathematics is built.

A first solution came from Ernst Zermelo. A definitive answer came from Kurt Gödel.