Difference between revisions of "1986 AHSME Problems/Problem 10"
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\textbf{(E)}\ \text{E} </math> | \textbf{(E)}\ \text{E} </math> | ||
− | ==Solution== | + | ==Solution 1== |
+ | We could list out all of the possible combinations in dictionary order. | ||
+ | |||
+ | <math>73rd:</math> MAEHS | ||
+ | <math>74th:</math> MAESH | ||
+ | <math>75th:</math> MAHES | ||
+ | <math>76th:</math> MAHSE | ||
+ | <math>77th:</math> MASEH | ||
+ | <math>78th:</math> MASHE | ||
+ | <math>79th:</math> MEAHS | ||
+ | <math>80th:</math> MEASH | ||
+ | <math>81th:</math> MEHAS | ||
+ | <math>82th:</math> MEHSA | ||
+ | <math>83th:</math> MESAH | ||
+ | <math>84th:</math> MESHA | ||
+ | <math>85th:</math> MHAES | ||
+ | |||
+ | We find that the 85th combination ends with the letter S. | ||
+ | So the answer is <math>\textbf{(C)}\ S</math>. | ||
== See also == | == See also == |
Revision as of 15:16, 24 February 2016
Problem
The permutations of the are arranged in dictionary order as if each were an ordinary five-letter word. The last letter of the th word in this list is:
Solution 1
We could list out all of the possible combinations in dictionary order.
MAEHS MAESH MAHES MAHSE MASEH MASHE MEAHS MEASH MEHAS MEHSA MESAH MESHA MHAES
We find that the 85th combination ends with the letter S. So the answer is .
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.