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

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

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


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.

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?

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?

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).

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.