A1.　994 cages each contain 2 chickens. Each day we rearrange the chickens so that the same pair of chickens are never together twice. What is the maximum number of days we can do this　?

A2.　The real polynomial p(x) = xⁿ - nx^n-1 + (n²-n)/2 x^n-2 + a_n-3x^n-3 + ... + a₁x + a₀ (where n > 2) has n real roots. Find the values of a₀, a₁, ... , a_n-3.

A3.　The plane is dissected into equilateral triangles of side 1 by three sets of equally spaced parallel lines. Does there exist a circle such that just 1988 vertices lie inside it　?

B1.　The sequence of reals x₁, x₂, x₃, ... satisfies x_n+2 <= (x_n + x_n+1)/2. Show that it converges to a finite limit.

B2.　ABC is an acute-angled triangle. Tan A, tan B, tan C are the roots of the equation x³ + px² + qx + p = 0, where q is not 1. Show that p ≤ √27 and q > 1.

B3.　For a line L in space let R(L) be the operation of rotation through 180 deg about L. Show that three skew lines L, M, N have a common perpendicular iff R(L) R(M) R(N) has the form R(K) for some line K.