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.
