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34. C.W. Trigg, (Equal n-sectors), Solution of problem 146, National Mathematics

Magazine, 12 (April 1938), 353-354.

35. C.W. Trigg, (Equal external bisectors), Solution of problem 224, National

Mathematics Magazine, 14 (Oct. 1939), 51-52.

36. C.W. Trigg and G.A. Yanosik, Two solutions of problem E350, American Mathe

matical Monthly, 46 (Oct. 1939), 513-514.

PROBLEMS--PROBLEMES

Problem proposals, preferably accompanied by a solution, should be sent to the editor, whose name appears on page 187.

For the problems given below, solutions, if available, will appear in EUREKA tool. 3, No. 2, to be published around Feb. 15, 1977. To facilitate their consideration, your solutions, typewritten or neatly handwritten on signed, separate sheets, should be mailed to the editor no later than Feb. 1, 1977.

181. Proposed by Charles W. Trigg, San Diego, California.

A polyhedron has one square face, two equilateral triangular faces attached to opposite sides of the square, and two isosceles trapezoidal faces, each with one edge equal to twice a side, e, of the square. What is the volume of this pentahedron in terms of a side of the square?

182 , Proposed by Charles W. Trigg, San Diego, California.

A framework of uniform wire is congruent to the edges of the pentahedron in the previous problem. If the resistance of one side of the square is 1 ohm, what resistance does the framework offer when the longest edge is inserted in a circuit?

183, Proposed by Viktors Linis, University of Ottawa.

If x + y = 1, show that

x m+1 n c) jCj + n+1 m` xi~i = 1

=oy m +j y i L8 n+i

holds for all m, n = 0,1,2,...
This problem is taken from the list submitted for the 1975 Canadian Mathematical Olympiad (but not used on the actual exam).
184, Propose par Hippolyte Charles, Waterloo, Quebec.

Si I = {X E R I a s x s b) et si la fonction f : 1 .I est continue, montrer que 1'equation f(x) = x admet au moins une solution dans I.