The following problem was included in the paper set in the Mathematical Tripos on the morning of January 5, 1881 :

iii. Prove that, if a + b + c = 0 and x + y + z = 0, then 4(ax + by + cz)3 - 3(ax+ by + cz)( a2+ b2+ c2)(a2+ y2 + z2) - 2 (b - c) (c - a) (a - b)(y - z) (z - x) (z - y)=54abcxyz.

A solution of this problem was published by A. Cayley in June 1881 ; see the Messenger of Mathematics, XI. (1882), 23-25. Cayley's solution took the form of a long and cumbrous verification, and he admitted that he did not know the origin of the result nor did he see any simple way of proving it.