While digging through some dusty corners of my file cabinet, I found a photocopied sheet of eight (handwritten) problems from 1985 that I recall receiving from my secondary school mathematics teacher way back when. Four of the problems are labeled "Set U" and the other four are labeled "Set V". I'm reproducing "Set U" below, but I'm not asking for solutions to the problems; rather, my question is,
Where can I find the other problems in this series?
Presumably the series started with "Set A"? Some further information: At the bottom of Set U, it says to send solutions to D. M. Hallowes, 17 St. Albans Road, Halifax before 1st June, and at the bottom of Set V, it says to send solutions to F. J. Budden, 15 Westfield Ave., Gosforth, Newcastle upon Tyne by Oct 1st.
Here are the problems in Set U.
U1. Given $\cos \alpha + \cos\beta = 1$. Prove that $${\cos \beta \cos(\alpha/2) \over \cos(\beta-\alpha/2)} + {\cos \alpha \cos(\beta/2) \over \cos(\alpha - \beta/2)} = 1.$$
U2. ABCD is a general quadrilateral with squares described outwards on the four sides. These squares have centres W, X, Y, Z which form a second quadrilateral. Each quadrilateral has two diagonals. Prove that the midpoints of the four diagonals form a square.
U3. Find all the triangles with integral sides and integral area such that the area is numerically equal to the perimeter.
U4. Two rectangles are described as incomparable if neither can be placed inside the other when they are aligned so that corresponding sides are parallel. Prove or disprove the statement, "No rectangular region can be tiled with mutually incomparable rectangles."
