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Unable to solve,plz help.

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by harsh.champ » Thu Feb 04, 2010 5:50 am
For a positive integer n, let Pn denote the product of the digits of n, and Sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which Pn + Sn = n is


(1)81
(2)16
(3)18
(4)9
(5)27


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I am unable to find any method to solve such type of questions?
Is there any formal and proper method/technique ??
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by ajith » Thu Feb 04, 2010 6:06 am
(1)81
(2)16
(3)18
(4)9
(5)27


_______________________

I am unable to find any method to solve such type of questions?
Is there any formal and proper method/technique ??[/quote]


for two digit numbers in the form ab

Pn = ab
Sn = a+b

Pn + Sn = ab+a+b

ab+a+b = 10a+b

ab = 9a

b=9

19 follows the rules
so does 29..39....99

9 numbers in total

For 3 digit numbers
abc

Pn = abc
Sn = a+b+c
abc+a+b+c = 100a+10b+c
abc = 99a+9b
abc = 9(11a+b)

for a =1
bc = 99 +9b {not possible}
for a=2
2bc = 198+b

not possible ...

.
.
.
for a=9
9*bc = 891+ 9b
not possible

So, 9 is the answer
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