perplexus.info :: Numbers : Number = Sum (Digit)*Product (Digit)

Number = Sum (Digit)*Product (Digit) (Posted on 2010-06-21)

N is a positive base ten integer having at least 2-digits but at most 4-digits, which is obtained by multiplying the sum of its digits with the product of its digits. It is known that N cannot contain any leading zero.

Determine all possible value(s) of N.

Submitted by K Sengupta

Rating: 4.0000 (2 votes)

Solution: (Hide)

135 and 144 are the only possible values of N, that satisfy the given conditions, since:
(1+3+5)(1*3*5) = 9*15 = 135
(1+4+4)(1*4*4) = 9*16 = 144
For an explanation, refer to:
The solution submitted by Jer in this location.
The solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: No Subject... Too late to be sorry...	Ady TZIDON	2010-06-24 10:25:15
this 'N that	ed bottemiller	2010-06-22 12:55:01
re: No Subject	Charlie	2010-06-21 23:20:08
re: Solution & thoughts	Daniel	2010-06-21 21:11:59
No Subject	ed bottemiller	2010-06-21 17:09:38
re: Count em up!	Charlie	2010-06-21 16:32:42
Count em up!	ed bottemiller	2010-06-21 15:10:20
re: Solution & thoughts	Charlie	2010-06-21 14:22:24
Solution & thoughts	Jer	2010-06-21 14:09:07
Non-leading zero??	ed bottemiller	2010-06-21 13:28:57

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