perplexus.info :: Numbers : Four Elements

Four Elements (Posted on 2013-02-14)

At one period the Ancients recognised four elements:

                Fire
             Air    Earth
                Water

Solve the following base10 alphametric when the elements are in balance according to:
FIRE + EARTH = AIR + WATER,
and AIR wholly divides FIRE.

Note that by ignoring "AIR wholly divides FIRE" there are three other solutions to the alphametric.

Analytical solutions (PnP) can be reasonably achieved.

Submitted by brianjn

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Solution: (Hide)

earth fire water air earth + fire
41802 9384 51048 138 51186
Lesser solutions:
41832 9684 51348 168 51516
61402 9846 71064 184 71248
14805 9681 24018 468 24486

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	In the absence of a PnP solution (spoiler).	Charlie	2013-02-15 14:33:37

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