# EDU physics Mathematical Mar GMT Jo

## Found at: 0x1bi.net:70/textfiles/file?humor/puzzle.spo

```Article 596 of sci.physics:
```
```From: TS0014%OHSTVMA.BITNET@CUNYVM.CUNY.EDU
```
```Newsgroups: sci.physics
```
```Subject: Re: Mathematical Puzzle]
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```Message-ID: <903@sri-arpa.ARPA>
```
```Date: 21 Mar 88 18:28:19 GMT
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```Lines: 21
```

```From:  Joe Damico
```

```Assuming the integers must be "different", it follows that:
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```---------------------------------------------------------------------
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```                              3,4  3,5  3,6
```
```                                        4,5
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```(IF sum=5 then numbers could be 1 and 4, and so P could know the numbers)
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```(IF sum=6 then numbers could be 1 and 5, again, P could know the numbers)
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```SO the numbers could be 1 and 6.
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```or (1,6)
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```By saying "I know that P doesn't know", S informs P that the sum is not 5.
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```But, by similar argument, the numbers could be 1 and 8.
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```Correct me if I'm wrong, but I don't think the problem has a unique solution
```
```->Joe Damico
```

```Article 599 of sci.physics:
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```From: stewart@cod.NOSC.MIL (Stephen E. Stewart)
```
```Newsgroups: sci.physics
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```Subject: Re: Mathematical Puzzle]
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```Message-ID: <1039@cod.NOSC.MIL>
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```Date: 22 Mar 88 23:53:07 GMT
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```References: <898@sri-arpa.ARPA> <5818@watdragon.waterloo.edu>
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```Reply-To: stewart@cod.nosc.mil.UUCP (Stephen E. Stewart)
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```Organization: Naval Ocean Systems Center, San Diego
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```Lines: 41
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```>In article <898@sri-arpa.ARPA> Richard Pavelle
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```>writes:
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```>>
```
```>>	P:  I don't know what the numbers are.
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```>>	S:  I knew you didn't.  Neither do I.
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```>>	P:  Oh! Now I know.
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```>>	S:  Oh! So do I.
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```>>
```
```>>What are the two integers?
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```>
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```>1 and 4
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```>
```
```>1=>product not prime or 1
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```>2a=>sum odd
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```>2b=>sum > 3
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```>3=>product is product of 2 primes since only two ways of getting product
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```>4=>sum < 7 since only 2 ways of getting sum
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```>
```

```than two ways of getting the product are allowed as long as all but one
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```are eliminated by the requirement that the sum be odd.  Any product of
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```two or more primes will be odd unless one (or more) of them is 2.
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```Thus, unless a 2 is involved, the sum of 1 plus the product and the sum
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```of any two numbers derived by taking subproducts will always be even
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```and 2a would not be satisfied.  So, at least one of the prime factors
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```must be a 2.  In this case, the sum of 1 plus the product will be odd.
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```But, unless all of the prime factors are twos, at least one pair of
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```numbers derived by taking subproducts of the prime factors will also
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```namely 1 and the product itself.  Thus, 2a gives P the answer.  From
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```the knowledge that P then knows the two numbers, S will be able to
```

```Steve Stewart
```

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