Difference between revisions of "2015 AIME II Problems/Problem 3"
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Let <math>m</math> be the least positive integer divisible by <math>17</math> whose digits sum to <math>17</math>. Find <math>m</math>. | Let <math>m</math> be the least positive integer divisible by <math>17</math> whose digits sum to <math>17</math>. Find <math>m</math>. | ||
| − | ==Solution== | + | ==Solution 1== |
| + | The three-digit integers divisible by <math>17</math>, and their digit sum: <cmath> | ||
| + | \begin{array}{c|c} | ||
| + | m & s(m)\\ | ||
| + | 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} | ||
| + | </cmath> | ||
| + | |||
| + | Thus the answer is <math>\boxed{476}</math>. | ||
== See also == | == See also == | ||
{{AIME box|year=2015|n=II|num-b=2|num-a=4}} {{MAA Notice}} | {{AIME box|year=2015|n=II|num-b=2|num-a=4}} {{MAA Notice}} | ||
Revision as of 13:00, 26 March 2015
Problem
Let 
be the least positive integer divisible by 
whose digits sum to . Find .
Solution 1
The three-digit integers divisible by , and their digit sum:
\[\begin{array}{c|c}
m & s(m)\\
102 & 3
119 & 11
136 & 10
153 & 9
170 & 8
187 & 16
204 & 6
221 & 5
238 & 13
255 & 12
272 & 11
289 & 19
306 & 9
323 & 8
340 & 7
357 & 15
374 & 14
391 & 13
408 & 12
425 & 11
442 & 10
459 & 18
476 & 17
\end{array}\] (Error compiling LaTeX. Unknown error_msg)
Thus the answer is 
.
See also
| 2015 AIME II (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
