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For how many three-digit positive integers is the sum of the digits equal to 5

gueesstt  Apr 10, 2018
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 #1
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-1

I get 8 as follows: {1, 0, 4} | |{1, 4, 0}{2, 0, 3}| {2, 3, 0} |{3, 0, 2} || {3, 2, 0} |{4, 1, 0} || {4, 0, 1}

Guest Apr 10, 2018
 #2
avatar+85757 
+2

The possible sums are

1+ 4 + 0

2+ 2 + 1

3 + 1 + 1

3 + 2 + 0

5 + 0 + 0

 

So....the possible integers are

104, 113, 131, 122, 140, 203, 212, 221,230, 302, 311, 320, 401, 410, 500

 

I get 15

 

 

cool cool cool

CPhill  Apr 10, 2018
 #3
avatar+19207 
+2

For how many three-digit positive integers is the sum of the digits equal to 5

 

Three-digit integer: \(abc\)


\(\text{ $1\le a \le 5$ }\\ \text{ $0\le b \le 4$ }\\ \text{ $0\le c \le 4$ and $c=5-(a+b)$ } \)

 

\(\begin{array}{|c|c|c|c|c| } \hline & b=0 & b=1 & b=2 & b=3 & b=4 \\ \hline a=1 & c=4 & c=3 & c=2 & c=1 & c=0 \\ a=2 & c=3 & c=2 & c=1 & c=0 \\ a=3 & c=2 & c=1 & c=0 \\ a=4 & c=1 & c=0 \\ a=5 & c=0 \\ \hline \end{array} \)

 

15 possible integers

\(\begin{array}{ c c c c c } & 104 & 113 & 122 & 131 & 140 \\ & 203 & 212 & 221 & 230 \\ & 302 & 311 & 320 \\ & 401 & 410 \\ & 500 \\ \end{array}\)

 

 

laugh

heureka  Apr 11, 2018

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