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.