Difference between revisions of "1958 AHSME Problems/Problem 14"
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| − | After inspection, we notice a general pattern: the <math>n^ | + | After inspection, we notice a general pattern: the <math>n^t^h</math> boy dances with <math>n + 4</math> girls. |
Since the last boy dances with all the girls, there must be four more girls than guys. | Since the last boy dances with all the girls, there must be four more girls than guys. | ||
Revision as of 00:50, 22 December 2015
Problem
At a dance party a group of boys and girls exchange dances as follows: one boy dances with 
girls, a second boy dances with 
girls, and so on, the last boy dancing with all the girls. If 
represents the number of boys and 
the number of girls, then:
Solution
After inspection, we notice a general pattern: the $n^t^h$ (Error compiling LaTeX. Unknown error_msg) boy dances with 
girls.
Since the last boy dances with all the girls, there must be four more girls than guys.
Therefore, the equation that relates them is 
See Also
| 1958 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
