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Which number is 6 times the sum of its digits?

Question #101792. Asked by nibbles0011.

avatar
CapainNemo
Answer has 3 votes
CapainNemo
15 year member
105 replies avatar

Answer has 3 votes.
6 x (5+4) = 54

Dec 19 2008, 8:28 AM
Original22
Answer has 4 votes
Original22
16 year member
26 replies

Answer has 4 votes.
Yes, its 54.

SUM OF DIGITS: 5+4=9; 9*6=54

Dec 19 2008, 11:46 AM
avatar
looney_tunes star
Answer has 5 votes
Currently Best Answer
looney_tunes star
18 year member
3287 replies avatar

Answer has 5 votes.

Currently voted the best answer.
There is another (although somewhat trivial) answer - zero. Considering the problem as a Diophantine equation, the possibility of the number having 1, 2, 3 or more digits must be considered. It can be shown fairly readily that the 1-digit solution is 0, the only 2-digit solution is 54, and there are no solutions with 3 or more digits. These are the relevant equations:

1-digit (the number is a): a = 6a
2-digit (the number is ab): 10a + b = 6(a+b)
3-digit (the number is abc): 100a + 10b + c = 6(a+b+c)


link https://en.wikipedia.org/wiki/Diophantine_equation

Dec 19 2008, 5:11 PM
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