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        riddles >> easy >> Exchange Pairs to Get Square
        
(Message started by: Barukh on Jul 22^nd, 2004, 8:54am)

Title: Exchange Pairs to Get Square
Post by Barukh on Jul 22^nd, 2004, 8:54am

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

Title: Re: Exchange Pairs to Get Square
Post by Eigenray on Jul 22^nd, 2004, 2:16pm

1. [hide]523814769[/hide]
2. [hide]1278563049, 1285437609, 1503267984, or 1532487609[/hide]
Or do you want a method to do it by hand?

Title: Re: Exchange Pairs to Get Square
Post by Barukh on Jul 23^rd, 2004, 1:02am

on 07/22/04 at 14:16:27, 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... ;)