Reprieve

It is the during the time of Henry VIII. A man is tried and condemned
to be executed.

"You will be sent to the Tower and will be executed within the next
seven days. But, to add to your punishment, you will not be told which
day will be your last. You will not know the date of your death until
the executioner comes for you."

The large smile appears accross the man's face as he says "Oh, thank
you, thank you, I'm saved!!"

Why?

Would I be right in assuming that all executions happened at day?

If so, then the man cannot be executed, because his sentence is logically inconsistent.

Suppose he is sentenced on the 1st of January. If he lived until the night of the 7th, he
would know he was going to be executed the next day, because he must be executed within
the seven days.

This is not allowed, since he would know his date of death in advance. Therefore he cannot
be executed on the 8th. As he knows this, he would know his date of death on the night of
the 6th.

He follows this line of reasoning back through the days, and since he is alive today, he knows
that he cannot be executed tomorrow, since he would know tonight, and not today, since he
would know now. He can neither be executed outside nor withn the seven days, because that
would contradict the first and second parts of the sentence respectively, so the sentence is
null and void.

I think this is the reasoning required, but I also think they would just kill him anyway. Once
he says 'I'm saved!' the executioner comes for him. Since he was expecting to live, say, for
many years after this date, this comes as a surprise so fulfils the requirements of the
sentence. Alternatively, if he is sentenced at night, he could be told 'you will remain in the
Tower until the day you die', which he will think is a life sentence. In fact it does not
contradict his earlier sentence, so he could be taken away and executed at any time in the
next seven days, at which time he would be taken by surprise (though at least this way he
isn't tortured by the prospect of imminent death!). All that matters is that he THINKS he is
not going to be executed.

I would agree with Acolyte that no matter how you look at this, the
man cannot escape execution with the information provided. Chrismo,
is there more to tell? For example, Henry VIII was so fixated on
himself that he only executed people on the eighth (VIII) day? If
there is more, please tell. Otherwise, I'm stumped.

Coyote

No, that's all there is to it. I remember reading this when I was a child
in a book by Johnny Ball (Zoe Ball's father for those who know of
her)... I couldn't remember exactly how it went so I just threw in
Henry VIII for a bit of colour.

I should have probably explained that he was misguided, of course.
like somehow the judge is going to say "I say, by the devil he's right!
How jolly silly of us. Ok, of you go..."

Okay, so what's the answer? It must be something we're all missing.

Coyote

Acolyte's original answer was correct!

He was correct in the answer and in the final result, regardless of the
logical problem! It seems he usually is. (No swelled heads, Acolyte!
People like chopping those off, too. lol.)

Coyote

Any swelling would soon be punctured by the barrage of lectures I'm going to be facing,
starting tomorrow. If my brain starts leaking incomprehensible Maths goo onto the forums,
please let me know.

Nice puzzle.
Just hang the man! He'll never expect it and so you never break your
word.

This puzzle, and others, can be found in a book titled "The
unexpected hanging" by Martin Gardner. Used to write a column on
mathematics for Scientific American. I think he has passed to the
great Platonic Solid in the Sky, which may explain why he no longer
writes a column. Always an interesting read way back when. May be
easy to find in a libary, I recommend highly.

And he's written an annotated guide to Alice in Wonderland, with all its
logical fun...

The crime was that he killed the executioner? He IS the executioner? I
dunno.

--Rein