The Unexpected Hanging Paradox

In this video we take a look at the unexpected hanging paradox, also known as the surprise exam paradox. Almost 100 papers have been published on the paradox, but there is still no agreement on what the correct solution is. Can you solve the paradox?

Sources and additional reading:

Music:
"Constancy Part Three"
Licensed under Creative Commons: By Attribution 3.0

[domgluhwein]

Executioner: **knocks on door**
Prisoner: "HA! I KNEW IT!"
Executioner: "aw man" **sad face and leaves**

[peterjg]

The judge eventually decided to give him the electric chair, leaving him both shocked and surprised.

[cmmr]

Or look at it this way: prisoner deduces that no day is possible, so the judge picking any day would be a surprise to the prisoner.

[tokatstorm]

The prisoner's fatal logical flaw is that he adds a final option, ie that the execution does not take place. Because of this it becomes possible that he can be executed on Friday, and still be surprised (since he was expecting to get off free), so he can no longer eliminate any other days.

[Guess_The_Number]

The fact the prisoner is analysing it so much and doesn't know means any day would be a surprise.

[butterplayz_yt]

*Gets Hanged on all five days*
Ha surprised you on that one huh

[daco]

Judge: "i wont tell you when we gonna execute you"
Prisoner: "Oh cmon dont leave me hangin'"

[nqrtzy]

Executioner: “aight you boutta die”
Prisoner: “knew it”
Executioner: “nvm you’re free to go”

[sumuqh]

I kinda started to like this prisoner. He was a good prisoner. May his logic rest in peace.

[joshuahenderson]

Sounds like too many people with doctorates are debating the meaning of “Surprise.”

[mng]

Well if he thinks he’s not gonna be hanged on any day, then any day would’ve been a surprise.

[nathangoedeke]

I interpreted the judge's statement as "a day of the week will be chosen at random, and you will not know the result of that random choice". The prisoner is correct that if he isn't hanged on Thursday, then the hanging is no longer a surprise, but that is based on the knowledge he will have on Thursday, while the judge's statement was based on his knowledge on Sunday.

[farazsm]

When a prisoner takes the word “surprise” too seriously 😐

[cchapa]

Actually, there is a third option:
1. Statement - you will be hanged by surprise.
2. Deduction - I cannot be hanged on any day because I cannot be surprised, thus I will not be hanged.
3. Outcome - The prisoner is surprised when he is hanged on Wednesday, thus rendering the judge's statement true.

So the third option is thus "Knowing the prisoner would come to the logical conclusion, the judge made a statement which would result in a self fulfilling prophesy by luring the prisoner into a false sense of safety."
Seems pretty straightforward to me; judge was just trolling him. Paradox solved!

[pote]

Solution: If he rules out every day, then any day will be a surprise. Just because the prisoner thinks that it's true doesn't mean that it is.

[williamhalsted]

Seems pretty simple. Friday is the only day he could not be surprised. The problem is his logic counts backwards from the end of the week to the beginning, but the week actually goes forward, not backwards. So when his hanging comes on a Tuesday, he would be surprised because it could have been on a Wednesday, Thursday, or Friday. I noticed other people mentioned a self-fulfilling prophecy in which he deceives himself into thinking he won't be hanged, and is therefore surprised when he is. I think this fits very well with what I think.

[epiccheeseman]

"the prisoner was then surprised when the executioner knocked on his cell"

Congratulations, you solved it on accident by using a poor choice of words. Because the prisoner believed it couldn't happen, he was surprised when it did happen

[Smfsableye]

The prisoner’s reasoning is faulty, and this isn’t a paradox at all. The reality is that no matter what day the prisoner “rules out”, the hanging will still come as a surprise.

[WavyCats]

This is the stupidest “paradox” I’ve ever heard of

I think the flaw is actually already present when the prisoner deduces he cannot be hung on the Friday. Because if he reaches Friday and thus is correct in his deduction he would still be surprised because he had deduced it was impossible. Just like what happened on the Wednesday. "Basically, if A happens and I think A is impossible because I would not be surprised, I would be surprised".