perplexus.info :: Numbers : Summing or Multiplying

Home > Numbers

Summing or Multiplying (Posted on 2006-08-21)

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)

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Thoughts

Comment 21 of 21 |

For the first part: YES, there are infinite such numbers,

Examples:

---------------

22, 2+2=2*2

123, 1+2+3 =1*2*3 =6

1124, 1+1+2+4 =1*1*2*4 =8

11125, 1+1+1+2+5 = 1*1*1*2*5= 10

111126, 1+1+1+1+2+6 = 1*1*1*1*2*6=12

1111127, 1+1+1+1+1+2+7= 1*1*1*1*1*2*7=14

Posted by K Sengupta on 2023-05-20 00:20:06

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info