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   Author  Topic: Exchange Pairs to Get Square  (Read 394 times)
Barukh
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Exchange Pairs to Get Square  
« on: Jul 22nd, 2004, 8:54am »		 Quote Quote Modify Modify
1. Digits from 1 to 9 are placed in natural order to form the number 123456789. It is required in as few exchanges of pairs of digits as possible to convert it into a square number.  
 
Example: the following sequence of 6 exchanges (78 )(84)(46)(69)(93)(32) gives the number 139854276, which is the square of 11826.
 
But it can be done in fewer exchanges.
 
2. What if 0 is added, and the original number is 1234567890?
 
Source: Dudeney
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Eigenray
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Re: Exchange Pairs to Get Square  
« Reply #1 on: Jul 22nd, 2004, 2:16pm »		 Quote Quote Modify Modify
1.  523814769
2.  1278563049, 1285437609, 1503267984, or 1532487609
Or do you want a method to do it by hand?
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Barukh
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Re: Exchange Pairs to Get Square  
« Reply #2 on: Jul 23rd, 2004, 1:02am »		 Quote Quote Modify Modify
on Jul 22nd, 2004, 2:16pm, Eigenray wrote:
Or do you want a method to do it by hand?

I didn't expect that. Afterall, I put it in Easy section...  Wink
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