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#5
11-20-2013, 06:41 PM
 zenobia43 Member Join Date: Mar 2012 Posts: 89

I think the difficulty stems from the fact that the Englishized clues don't state the missing logical terms (thankfully).

Ready for some tedium? If not, start another puzzle and have some more fun .

Let's take your clue 2 first:

"2) Of Vestor and the planet with a diameter of 650,000 mi., one orbits star PLC 120 and the other is 47 light years from earth."

If we isolate the relationship involving 47 light years, the clue is really:

47 = (Vestor AND (NOT 650)) OR ((NOT Vestor) AND 650)

This is just saying that if 47 is Vestor, 47 cannot also be 650, and if 47 is 650, it cannot also be Vestor. I have added the missing NOT terms.

Now we have our fully specified equation for 47.

We would like to replace Vestor and its inverse in this equation with the information we get from your clue 1. Let's find out what Vestor is, and then express its inverse.

"1) Vestor is either the planet with a diameter of 714,000 mi. or the exoplanet orbiting star PLC 120."

Written more completely with the missing NOT terms:

Vestor = (714 AND (NOT PLC)) OR ((NOT 714) AND PLC)

I.e. Vestor must be one and only one of the two alternatives given.

Now here's the tricky part.

When expressing Vestor in terms of two other logical variables that can be true or false (true means Vestor is equal to that element, false means Vestor is not equal to that element), there are four combinations. That is the entire universe of possibilities.

Clue 1 states that only two of the combinations are possible.

Then the inverse must be the remaining two combinations. The inverse includes "Vestor is both 714 and PLC" and "Vestor is neither 714 nor PLC."

Now we know what "NOT Vestor" (Vestor's inverse) is.

(NOT Vestor) = (714 AND PLC) OR ((NOT 714) AND (NOT PLC))

So let's get back to our equation for 47 and do some substituting.

Let's do the first term which is the easiest.

47 = Vestor AND (NOT 650) ...

Substituting for Vestor ...

47 = ((714 AND (NOT PLC)) OR ((NOT 714) AND PLC)) AND (NOT 650) ...

We know from your clue 2 that 47 cannot be PLC, so using some boolean algebra, this reduces to:

47 = (714 AND (NOT PLC)) AND (NOT 650) ...

Rearranging terms ...

47 = 714 AND (NOT 650) AND (NOT PLC) ...

Now let's take the second term of the equation for 47.

47 = ... OR ((NOT Vestor) AND 650)

Substituting for (NOT Vestor) ...

47 = ... OR (((714 AND PLC) OR ((NOT 714) AND (NOT PLC))) AND 650)

Again - since 47 cannot be PLC, we can reduce the above to:

47 = ... OR (NOT 714) AND (NOT PLC) AND 650

Rearranging terms ...

47 = ... OR (NOT 714) AND 650 AND (NOT PLC)

Now putting the two modified terms in the original equation together and bringing the common term, (NOT PLC), outside, we get ...

47 = (NOT PLC) AND ((714 AND (NOT 650)) OR ((NOT 714) AND 650))

We know that 47 is NOT PLC. So the NOT PLC term is true, and we can eliminate it.

Or as you put it more simply, 47 is either 714 or 650.

I have the uneasy feeling that I just proved that 1 = 2 by dividing by zero.

I glossed over some definitions, and I took great liberties by using boolean algebra to prove your thesis.

I'd much rather use the grid and the technique indicated by 2manynames in one of the original posts (06-09-2013, 08:40 AM) to solve the nominal logic puzzle. I usually screw something up if I try to use boolean algebra.

Last edited by zenobia43; 11-20-2013 at 08:52 PM.