# Sunday Times Teaser 2758 – Square Dance

*by Angela Newing*

#### Published: 2 August 2015 (link)

Dancers numbered from 1 to 9 were about to perform a square dance: five were dressed in red and the rest in blue. They stood in a 3-by-3 array with all three dancers in the first row wearing red and all three in another row wearing blue. Their numbers formed a magic square (ie, the sum of the three numbers in any row, column or diagonal was the same). One of the dancers in red looked around and noted that the sum of the numbers of the four other dancers in red was the same as the sum of the numbers of the four dancers in blue. One of the dancers in blue was number 8, …

… what were the numbers of the other three dancers in blue?

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At first I thought “the dancers around them” meant only those adjacent, but you can’t get a solution that way.

So I went with: “One dancer wearing red noticed that the sum of the numbers on the other dancers wearing red was the same as the sum of the numbers on the dancers wearing blue”, and that gives a unique solution. And the code is simpler.