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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?

See The Solution Submitted by e.g.    
Rating: 4.2500 (8 votes)

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simple solution to simple part | Comment 1 of 20
Any 2, 3, 4, etc digits between 2 and 9 can be chosen, and their product found. Intersperse as many 1's as needed to bring the total up to this product. (In the case of 2 and 2 no 1's will be needed.) This guarantees infinitely many such numbers.
  Posted by Charlie on 2006-08-21 09:52:08
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