Difference between revisions of "1992 AJHSME Problems/Problem 15"
Mrdavid445 (talk | contribs) (Created page with "==Problem== What is the <math>1992^\text{nd}</math> letter in this sequence? <cmath>\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots </cmath> <math>\text{(A)}\ \text{A} \qquad ...") |
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<math>\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}</math> | <math>\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}</math> | ||
| + | |||
| + | ==Solution== | ||
| + | The sequence consists of repeated strings of 9 letters, <math>\text{ABCDEDCBA}</math>. When 1992 is divided by 9, the remainder is 3, and so the 1992nd letter in the sequence is the 3rd letter of the smaller string, <math>\boxed{\text{(C)}\ \text{C}}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1992|num-b=14|num-a=16}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 00:09, 5 July 2013
Problem
What is the 
letter in this sequence?
![\[\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots\]](http://latex.artofproblemsolving.com/6/c/b/6cb4705ab4ed9971886fcc4ea9087c9d419a4942.png)
Solution
The sequence consists of repeated strings of 9 letters, 
. When 1992 is divided by 9, the remainder is 3, and so the 1992nd letter in the sequence is the 3rd letter of the smaller string, 
.
See Also
| 1992 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
