KöMaL 2009 K193

Four girls and four boys went dancing together. The first dance was a waltz. Each boy asked a girl to dance (each girl was only asked by one boy). The next dance was a tango. This time, it was the girls who asked the boys to dance. Each girl asked a boy (and each boy was asked by only one girl). There was no couple that danced both dances together. Given the following information, find out who danced each dance with whom. $a$) Charles waltzed with the girl who danced tango with Daniel. $b$) Andrew asked that girl to waltz who danced tango with the boy who waltzed with Emily. $c$) Bernard waltzed with the girl who danced tango with Mary's waltz partner. $d$) Gillian did not dance tango with Bernard. $e$) Helen danced tango with a boy who did not waltz with Gillian. After the two dances, when the dance instructor asked everyone to stand behind the back of the partner whom he or she asked to dance, the result was one big circle of people.