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Mike's Magical Scale


Best Answer Barcallica, 03 June 2013 - 03:37 PM

 

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

 

I don't think so. 5,1,1,1 also works. I think these are the only solutions

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#1 BMAD

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Posted 01 June 2013 - 09:55 PM

Mike has a magic scale, each side of which holds a positive integer.  He plays the following game: each turn, he chooses a positive integer n. He then adds n to the number on the left side of the scale, and multiplies by n the number on the right side of the scale. (For example, if the turn starts with 4 on the left and 6 on the right, and Mike chooses n = 3, then the turn ends with 7 on the left and 18 on the right.) Mike wins if he can make both sides of the scale equal. Show that if the game starts with the left scale holding 17 and the right scale holding 5, then Mike can win the game in 4 or fewer turns.

 


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#2 Barcallica

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Posted 02 June 2013 - 06:55 AM

Spoiler for Is it?


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#3 BMAD

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Posted 02 June 2013 - 06:39 PM

Spoiler for Is it?


That answer works. Is there a shorter answer, one that uses less numbers?
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#4 Barcallica

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Posted 03 June 2013 - 03:37 PM   Best Answer

 

Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

 

I don't think so. 5,1,1,1 also works. I think these are the only solutions


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#5 superprismatic

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Posted 04 June 2013 - 09:44 PM

 



 


Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

 

I don't think so. 5,1,1,1 also works. I think these are the only solutions

 

There are two others: 1,5,1,1 and 1,1,5,1.


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#6 BMAD

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Posted 05 June 2013 - 04:21 AM

 

 



 


Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

 

I don't think so. 5,1,1,1 also works. I think these are the only solutions

 

There are two others: 1,5,1,1 and 1,1,5,1.

 

But is there a three number solution?


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#7 superprismatic

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Posted 06 June 2013 - 01:15 AM

 

 

 



 


Spoiler for Is it?

That answer works. Is there a shorter answer, one that uses less numbers?

 

I don't think so. 5,1,1,1 also works. I think these are the only solutions

 

There are two others: 1,5,1,1 and 1,1,5,1.

 

But is there a three number solution?

 

No


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#8 Pickett

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Posted 06 June 2013 - 01:42 PM

Spoiler for My Findings


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#9 Pickett

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Posted 06 June 2013 - 02:00 PM

Spoiler for Quick Note...


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#10 BMAD

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Posted 13 June 2013 - 12:02 AM

Bonus points for Pickett though for awesome programming talents!


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