Difference between revisions of "2015 AIME II Problems/Problem 3"

(Solution 1)
(Solution 1)
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The three-digit integers divisible by <math>17</math>, and their digit sum: <cmath>
 
The three-digit integers divisible by <math>17</math>, and their digit sum: <cmath>
 
\begin{array}{c|c}
 
\begin{array}{c|c}
m & s(m)\\
+
m & s(m)\\ \hline
 
102 & 3 \\
 
102 & 3 \\
 
119 & 11\\
 
119 & 11\\

Revision as of 13:01, 26 March 2015

Problem

Let $m$ be the least positive integer divisible by $17$ whose digits sum to $17$. Find $m$.

Solution 1

The three-digit integers divisible by $17$, and their digit sum: \[\begin{array}{c|c} m & s(m)\\ \hline 102 & 3 \\ 119 & 11\\ 136 & 10\\ 153 & 9\\ 170 & 8\\ 187 & 16\\ 204 & 6\\ 221 & 5\\ 238 & 13\\ 255 & 12\\ 272 & 11\\ 289 & 19\\ 306 & 9\\ 323 & 8\\ 340 & 7\\ 357 & 15\\ 374 & 14\\ 391 & 13\\ 408 & 12\\ 425 & 11\\ 442 & 10\\ 459 & 18\\ 476 & 17 \end{array}\]

Thus the answer is $\boxed{476}$.

See also

2015 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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