IMO 1970 LL NET37

Origin: NET

Problem

Solve the set of simultaneous equations v2+ w2+ x2+ y2 = 6 −2u, u2+ w2+ x2+ y2 = 6 −2v, u2+ v2+ x2+ y2 = 6 −2w, u2+ v2+ w2+ y2 = 6 −2x, u2+ v2+ w2+ x2 = 6 −2y.