Vietnam 63/1 solution

2nd VMO 1963

Problem 1

A conference has 47 people attending. One woman knows 16 of the men who are attending, another knows 17, and so on up to the last woman who knows all the men who are attending. Find the number of men and women attending the conference.

Solution

Suppose there are m women. Then the last woman knows 15+m men, so 15+2m = 47, so m = 16. Hence there are 31 men and 16 women.

Thanks to Suat Namli

2nd VMO 1963