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Summing or Multiplying (Posted on 2006-08-21) Difficulty: 4 of 5
123 is a peculiar integer, because 1+2+3=1*2*3. 1412 is also peculiar, since 1+4+1+2=1*4*1*2.

A simple question: are there infinitely many such numbers?

A not so simple question: if so, are there such numbers for ANY number of digits?

  Submitted by e.g.    
Rating: 4.2500 (8 votes)
Solution: (Hide)
Yes, for the first one. You can add enough 1's at the beginning of any sequence of digits ABC...Z, you produce a number that satisfies both conditions.

But no, for the second one: a computer-aided search helps show that there are no 24, 34, 35, or 48 digits solutions, just for numbers with 50 digits or less.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Thoughts K Sengupta2023-05-20 00:20:06
re(3): Peculiars vs. PrimesOld Original Oskar!2006-08-23 07:24:50
re(4): Peculiars vs. PrimesOld Original Oskar!2006-08-23 07:23:09
re(3): Peculiars vs. PrimesRobby Goetschalckx2006-08-23 05:14:50
Some Thoughtsre(2): Peculiars vs. PrimesDej Mar2006-08-22 19:00:39
Some Thoughtsre: Peculiars vs. PrimesFederico Kereki2006-08-22 17:33:41
Peculiars vs. PrimesEric2006-08-22 16:32:36
re: An extra question -- spoilerCharlie2006-08-22 14:24:01
re(2): An extra question - solution (spoiler)Charlie2006-08-22 14:19:57
Solutionre: An extra question - solution (spoiler)Dej Mar2006-08-22 12:43:18
QuestionAn extra questione.g.2006-08-22 11:28:09
re(2): my not so simple solution -- OOPS!Daniel2006-08-22 06:05:03
Solutionre(2): With a programCharlie2006-08-21 22:32:07
re: my not so simple solution -- OOPS!Old Original Oskar!2006-08-21 21:54:01
Solutionre(2): With a programDej Mar2006-08-21 20:38:13
my not so simple solutionDaniel2006-08-21 19:33:03
Some Thoughtsre: With a programFederico Kereki2006-08-21 19:08:01
With a programJoe2006-08-21 16:45:01
Some ThoughtsCommentsFederico Kereki2006-08-21 12:36:44
Cursory examinationJer2006-08-21 10:03:34
simple solution to simple partCharlie2006-08-21 09:52:08
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