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Perfect Pairs/Trios


Best Answer Rob_G, 22 April 2014 - 08:09 PM

besides we are assuming that all numbers are distinct

 

Spoiler for Well...(edited)
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#1 BMAD

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Posted 22 April 2014 - 02:47 PM

Consider the following definitions of perfect pairs/trios.  If there exist such numbers that fit the definition show how many exist, if no number exists, provide a proof: (Each number is assumed to be distinct)

 

1. When you add two numbers you get a certain answer.  Using the same two numbers, subtract the larger from the smaller and get the same answer in the first sentence.

 

2.  Using three numbers, add the first two numbers together then divide the sum by the third number.  The result will be one of the three numbers.

 

3. Two numbers whose sum is equal to their quotient.


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#2 phil1882

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Posted 22 April 2014 - 03:36 PM

Spoiler for

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#3 BMAD

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Posted 22 April 2014 - 04:06 PM

Spoiler for

Remember if it is possible, to what extent is it possible, describe the total range of numbers


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#4 Rob_G

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Posted 22 April 2014 - 04:27 PM

Spoiler for Well...

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#5 BMAD

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Posted 22 April 2014 - 04:39 PM

Spoiler for Well...

0,0 is not the only possibility for #1


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#6 BMAD

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Posted 22 April 2014 - 04:48 PM

besides we are assuming that all numbers are distinct


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#7 Rob_G

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Posted 22 April 2014 - 08:09 PM   Best Answer

besides we are assuming that all numbers are distinct

 

Spoiler for Well...(edited)

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#8 Rob_G

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Posted 22 April 2014 - 08:31 PM

Oh...

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#9 BMAD

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Posted 22 April 2014 - 09:01 PM

counting posts #7 & #8 together that is


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