[net.lang.prolog] Another Puzzle

mckenney@orstcs.UUCP (09/12/83)

#R:sri-arpa:-485400:orstcs:23900001:000:660
orstcs!mckenney    Sep 10 01:14:00 1983

Hypothetical General Solution to "Another Puzzle"

	For any string of digits greater than 6 in length, the following
	solution is unique:

	x21y1000

	where "x" is replaced by <base - 4> and "y" is replaced by a
	string of <x - 7> zeros.  Note that a string of digits of base
	n will also be of length n.

	Examples:

		Base 7  -- 3211000
		Base 10 -- 6210001000
		Base 16 -- C210000000001000
	
	For bases 2 through 6, no solution exists.

	Now, I have no idea how one would go about programming this into
	a Prolog program of reasonable running time.  (I have produced
	a -very- informal (read probably bug-ridden) proof by hand).

			Paul
			orstcs!mckenney

mckenney@orstcs.UUCP (09/12/83)

#R:sri-arpa:-485400:orstcs:23900002:000:303
orstcs!mckenney    Sep 10 13:31:00 1983

Comments on Hypothetical General Solution

	It's a good thing I said "Hypothetical"!  Two more solutions
	not found by my proof:

		Base 4:	2020
		Base 5:	21200

	I obviously need to clean up my proof, will send it when and if.
	I look forward to seeing a Prolog solution.

				Paul
				orstcs!mckenney

loeb@uiuccsb.UUCP (09/17/83)

#R:sri-arpa:-485400:uiuccsb:9400002:000:45
uiuccsb!loeb    Sep 16 17:56:00 1983


  A solution to this is in net.ai, note 70.