$20$ people (boys and girls) attend a dance. The first boy dances with $5$ girls; the second boy dances with $6$ girls; the third boy dances with $7$ girls, and so forth. The last boy dances with all the girls.

How many attendees are boys and how many are girls?

Any ideas or hints how to approach this question?

  • 2
    $\begingroup$ If there are $n$ boys, then the last boy dances with $n+4$ girls. If this must be the same as all the $20-n$ girls, that gives you an equation. $\endgroup$ – Henning Makholm Nov 15 '15 at 21:06

So the $n$th boy is dancing with $n+4$ girls. If $n$ is the last boy then there are $n+4$ girls. In total then $n + n + 4 = 20$, so $n=8$. So there are $12$ girls, $8$ boys.


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