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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re(2): With a program | Comment 9 of 20 |
(In reply to re: With a program by Federico Kereki)

Indeed, with this program:

DEFDBL A-Z
CLS
FOR a = 1 TO 9
FOR b = a TO 9
FOR c = b TO 9
FOR d = c TO 9
FOR e = d TO 9
  p = a * b * c * d * e
  dig = p - (a + b + c + d + e) + 5
  IF dig > 10 AND dig < 30 THEN
    LOCATE 1, (dig - 10) * 4
    PRINT dig;
  END IF
NEXT
NEXT
NEXT
NEXT
NEXT

no 24-digit number is found.  The place on the screen reserved for 24 is empty.


  Posted by Charlie on 2006-08-21 22:32:07
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