`
`

`
`
*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.
`

`
`

`
`

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

*
*

*
*

*
*

*
*

*
*

*
*

*
*

`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.`

`
`