posted 05-12-2005 22:34            

A. I would be booked on one of the five flights.
B. I would not know in advance whether I was on a particular flight.

The details of the guarantee were staggering. I was to receive an iron-clad commitment from the airline, its flight partners, all its investment bankers, and all the national entities that they served - in the amount of US$100 Billion.

Naturally, I decided to accept the offer. I signed the necessary papers along with all the other participating parties.

Then I struck! I demanded immediate payment of the $100 Billion. I claimed that both guarantees, A & B, could not simultaneously be met. Can you guess why? Was I right? If not, where did I go wrong?

posted 05-13-2005 03:12               

That explanation seems too easy to me. Maybe there's another paradox here that I'm not seeing yet.

The other one I thought of .. if you are actually booked on one of the flights, then you could find out in advance which flight you are booked on, which conflicts with the second statement. Since the second statement can't ever be true unless they violate the first statement, then they can never comply with both statements. This is not that different than my first explanation, but I think my first explanation makes more sense, but they are both use the same logic.

-David

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posted 05-13-2005 07:18               

2 - With the last flight eliminated, the same applies to the 4th flight. Following the 3rd flight you know you must be on the 4th flight for condition 2 to hold true. This eliminates Flight 4.

3 - The same flow of logic applies to flights 3 and 2, leaving you only with the option of being on the first flight.

However, I suspect there is a small problem with the logic, but I can't place it, so you could probably make that argument to the airline, and it would hold.

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Melinda Towne

posted 05-13-2005 11:42               

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Steve Nelson

posted 05-13-2005 14:38               

quote:

---

Originally posted by JosephP:

A. I would be booked on one of the five flights.
B. I would not know in advance whether I was on a particular flight.

---

I know you said you constructed this puzzle on a well-known logical paradox, but I'm quite unfamiliar with any well-known logical paradox, I'm going to stick with my original answer based merely on language.

What was meant by point B?

That you would not know in advance of any particular flight whether or not you would be on it?

Or, you would not know in advance of all flights on which one you would be.

I understood it in the first manner. Thus, after the fourth flight took off and you were still sitting at the gate waiting for your name to be called, you would understand, based on A, that you would be on the fifth flight.

Perhaps wording "B" with a little more clarity would end the confusion.

But then, again, now my head's spinning with all kinds of other thoughts and maybe it doesn't even matter how B was intended.

ah well.

posted 05-13-2005 14:45               

Therefore, you sit in the airport convinced that you are not booked on any flight and will collect your guarantee because the airline is defaulting on condition A.

You are then very surprised to hear your name called for the (for instance) 3:00 PM flight. After all, you had already eliminated this (and every other) possibility through earlier reasoning. With your surprise, your dreams of wealth vanish!

posted 05-13-2005 18:23               

The assumption that we cannot be on the 4th flight is based on the presumtion that it has become the last flight we can be on - but it has not. Precisely because we can eliminate ALL 5 flight, the seeming paradox is eliminated. The only flight we cannot be on is the 5th. I just had to think about it a little more.

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Melinda Towne

posted 05-13-2005 21:03               

I'm going to bed!!!

posted 05-14-2005 05:33               

Because we can eliminate ALL the flights, we can actually eliminate none, purring us back to square one. The flights have to be treated as a group, not individually. The only point at which there is only 1 flight we could be booked on is after the 4th flight has been called. Thus that is the only time when we could be certain.

It's sort of the like the question of Anchimedes and the Tortois. You have a race, giving the Tortoise a head start. Archimedes must always reach the Tortoise's starting point before he can pass it. By that point, the Tortoise has moved forward. Archimedes must then move to the Tortoises new "starting point" at which point it has again moved forward. Using this logic, Archimedes can never catch up to the Tortoise. If we change our perspective, we realize our conclusion is incorrect.

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Melinda Towne

posted 05-16-2005 12:39               

We say we know we are on the 4th flight - they say no we don't because we are on the 5th flight, but we cannot know for certain that they plan to break one of the rules until the 4th flight has left. We can only place ourselves on the 4th flight if we assume they are going to follow the rules - but here's the hitch: at that point, putting us on the 4th flight means we knew ahead of time, putting us on the 5th flight means we WILL know ahead of time, but we would have been WRONG before the 4th flight. Thus we still cannot be certain we are on the 4th flight until it leaves without us.

Thus as long as they put you on one of the first 4 flights, they are safe.

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Melinda Towne

posted 05-18-2005 07:20               

Here's why -

After the 2nd flight, there are 3 options. You believe you must be on the 3rd or 4th flight because placing you on the 5th flight violates the conditions or the problem.

But must you be on the 3rd flight? Or can you still be on the 4th flight? You would like to eliminate the 4th flight because you claim you would know you are not on the 4th flight. But for that argument to hold, you are claiming they are violating the conditions in order to NOT violate the conditions.

So now we have established that they plan to violate the conditions in one way or another. Because of this, we now have to know in what way they plan to violate the conditions. Because we eliminated each flight as a violation of the conditions, we must consider if we can determine which flight we will be on. The only flight we will be able to say we are on before the names are called is the last one. In other words, there is a time before that flight leaves that we can announce with certainty that we know we are on that flight. The same does not apply to any of the other flights.

I may not be explaining adequately, but it has to do with conditional logic. Logic does not always flow as easily as it appears. There is something wrong with eliminating the 4th flight on the assumption that the 5th is already eliminated - each flight must be considered as a part of the whole, not just a part of what is left after eliminating other flights.

If you are given a true coin, and toss it 99 time, all coming up heads, while you may want to argue that the next flip is most likely to be heads, I can pose an equally valid argument that it will be tails. The truth is that head/tails are equally likely if it is a true coin. Your perspective is that it is not a true coin, and thus is weighted toward heads. My perspective is that it is due to fall on a tails. Neither is correct.

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Melinda Towne

posted 05-18-2005 08:28            

You are a prisoner due for execution. The prison warden guarantees that

A: You will be executed on one of the next five days.
B: You will not know in advance which day that will be.

Day 5 comes and you say to yourself...

"Ah ha. They can't be executing me today because that would violate B. Thus, they won't be executing me at all."

The warden comes in an executes you. You did not expect this.