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Optimusprime
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Logic Fun and Math

12/15/2010 7:54 AM

Pandora's Box I.

Once upon a time, there was a girl named Pandora, who wanted a bright groom so she made up a few logic problems for the wannabe. This is one of them. Based upon the inscriptions on the boxes (none or just one of them is true), choose one box where the wedding ring is hidden.

Golden box

The ring is in this box.

Silver box

The ring is not in this box.

Lead box

The ring is not in the golden box.

Pandora's Box II.

And here is the second test. At least one inscription is true and at least one is false. Which means the ring is in the...

Golden box
The ring is not in the silver box.

Silver box

The ring is not in this box.

Lead box

The ring is in this box.

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Anonymous Hero
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#1

Re: Logic Fun and Math

12/15/2010 8:21 AM

The ring is in the golden box.

You can set up a truth table for the first case as follows:

BOX State

GB T F F F

SB F T F F

LB F F T F

The results of those tests as a Y = Possible and a N = Not Possible. For a Y all three statements must be true and false as described. In other words, if the first case is statement 1 is True and the other two statements are not True, then we assign a Y to that column. Consequently, if two statements are contradictory, then we assign a N.

.. Y N Y N

This means that the Golden Box or the Silver Box are the only two candidates that can have the ring. The other two cases the logic is contradictory.

The second test is more complex, but we can eliminate all cases where the Lead Box truth table is TRUE, because of the tests in the first case. However, all possible combinations for the second test are as follows:

BOX State

GB T F F F T F T

SB F T F F T T F

LB F F T F F T T

The results of those tests as a Y = Possible and a N = Not Possible are:

.. Y N N N N N N

Only the first test in the series can pass either based on the case two logic for the questions or elimination of the Lead Box.

Open the Golden Box and hope she doesn't turn out to be a witch after the honeymoon wears off and he doesn't leave the toilet seat up.

NOTE: If I screwed this up I really don't care. There are plenty of fish in the sea. ;-)
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kramarat
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#2

Re: Logic Fun and Math

12/15/2010 9:08 AM

Pandora doesn't deserve a bright groom............What kind of dummy buys her own wedding ring?

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ozzb
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#3
In reply to #2

Re: Logic Fun and Math

12/15/2010 10:15 AM

One that didn't buy it but inherited from her grandmother and want it to be the ring she was married with.

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kramarat
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#5
In reply to #3

Re: Logic Fun and Math

12/15/2010 10:29 AM

What can I say? I took the risk.

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Tornado
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#4

Re: Logic Fun and Math

12/15/2010 10:20 AM

Problem 1

If the ring is in the golden box, the statements are respectively TTF; if in the silver box FFT; if in the lead box FTT. Thus it is in the silver box.

Problem 2

If the ring is in the golden box, the statements are respectively TTF; if in the silver box FFF; if in the lead box TTT. Thus it is in the golden box.

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charsley99
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#6

Re: Logic Fun and Math

12/15/2010 12:41 PM

Tornado has it right according to the precursors of one or none and 1 true 1 false.

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passingtongreen
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#7

Re: Logic Fun and Math

12/15/2010 2:16 PM

I'm more interested in how different people got to their answers than the actual answers. I didn't meet a truth table till a decade or so ago, and I still find them less than obvious. My approach was...well it was like this:

Pandora 1. Gold and lead disagree ergo one is telling the truth ergo Silver must be lying ergo it is in the silver box.

Pandora 2. If it was in silver they would all be lying; if it was in lead they would all be telling the truth ergo the ring is in the gold box.

It looks as though we did the same or similar but expressed them differently.

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charsley99
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#8
In reply to #7

Re: Logic Fun and Math

12/15/2010 4:29 PM

You did a truth table in your head. You just didn't write it down.

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English Rose
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#9
In reply to #7

Re: Logic Fun and Math

12/16/2010 4:02 AM

That's how I did it

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glrusl
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#10
In reply to #7

Re: Logic Fun and Math

12/16/2010 8:53 AM

I also did it this way... I do visuals... The more senses I can involve, the better I can work things out.

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JBTardis
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#11

Re: Logic Fun and Math

12/16/2010 6:20 PM

Pandora's Box I.
Silver Box

Pandora's Box II.
Gold

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