another interesting math riddle
01-14-2018, 07:10 AM
Post: #11
 Joe Horn Senior Member Posts: 1,841 Joined: Dec 2013
RE: another interesting math riddle
(01-13-2018 10:03 AM)Didier Lachieze Wrote:  ... any number with more 7 digits cannot meet the criteria as it is superior to the maximum sum of its digits factorials (9!*8 has only 7 digits and is lower than any 8-digit number) and that for 7 digit numbers only the ones below 9!*7 (2540160) are candidates.

That's true in base 10, but if we extend the riddle to larger bases, it allows the factorials to be larger. For example, both 1441 and 1442 are solutions in base 15:

#1441d = #661(15) = 6! + 6! + 1!
#1442d = #662(15) = 6! + 6! + 2!

Unfortunately there don't seem to be ANY solutions which include a digit > 9, regardless of base. Strange.

<0|ΙΈ|0>
-Joe-
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 Messages In This Thread another interesting math riddle - Don Shepherd - 01-13-2018, 01:37 AM RE: another interesting math riddle - Gerson W. Barbosa - 01-13-2018, 02:04 AM RE: another interesting math riddle - Joe Horn - 01-13-2018, 06:02 AM RE: another interesting math riddle - Don Shepherd - 01-13-2018, 06:14 AM RE: another interesting math riddle - SlideRule - 01-13-2018, 12:47 PM RE: another interesting math riddle - Don Shepherd - 01-13-2018, 03:34 PM RE: another interesting math riddle - Didier Lachieze - 01-13-2018, 10:03 AM RE: another interesting math riddle - olr - 01-13-2018, 09:08 PM RE: another interesting math riddle - Didier Lachieze - 01-13-2018, 10:29 PM RE: another interesting math riddle - Didier Lachieze - 01-17-2018, 11:59 PM RE: another interesting math riddle - Joe Horn - 01-14-2018 07:10 AM RE: another interesting math riddle - SlideRule - 01-13-2018, 05:28 PM RE: another interesting math riddle - Gamo - 01-14-2018, 10:22 AM RE: another interesting math riddle - grsbanks - 01-14-2018, 10:44 AM

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