Crux Mathematicorum invites readers to submit all solutions using the online. This issue is restricted to active Crux subscribers. However, items in this. Crux Mathematicorum is a scientific journal of mathematics published by the Canadian Mathematical Society. It contains mathematical problems for secondary.

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Dworschak, Algonquin College; G. Hence it cannot be a perfect square. Theproblem then resurfaced in [5,6,7,11]. Kaye, Department of National Defence; F.

Elichuk’s solutions there were four different ones were more in thenature of poking gentle fun at the proposer, who seems to be an old acquaintance mathemtaicorum, for proposing what appeared to be a frivolous problem.

A 1’aide d’un compas seulement, determiner le centre inconnu d’un cercledonne.

Henderson, A classic problem in Euclidean geometry, J. Comment by Leo Sauves Algonquin College. Solution by the proposer. Ten pentagons have 50 sides and 50 interior angles. Ross Honsberger writes that “for interesting elementary problems, this publication is in a class by itself”.

To adequately describe the complete solutionof 1two important facts, which are implicit in 3must be brought out. Crux Mathematicorum invites readers to submit all solutions using the online submission form. Theproblem was followed by an outline of a proof by induction. There is a well-known formula for the sum of all the combinations of nn objects: Kaye, Department ofNational Defence. The sign of b can be cruux by specifying the sign ofr. Which of the following are divisible by 6 for all positive integers n?

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On peut maintenant demontrer que la suite A a la propriete desiree. Acknowledgments, I obtained references l, 2 from [15]; references 3, 7, 9, 17 from [20]; maghematicorum erence 4 from [5]; reference 6 from [11]; reference 8 from [14]; reference 10 from [16]; reference 12 from [13]; all the remaining references are my own.

### CRUX: Volume 43 Number 9

The inequality clearly holds for n-l. Leon Bankoff, unpublished as of manuscript on the history of theButterfly Problem. Problem in this issue solicits your answer to this question. Aspects ofsalesmanship are as varied as the personalities mathematiccorum teachers themselves.

## Problem 3980 from Crux Mathematicorum

Montrer que le cube de tout nombre rationnel est egal a la differencedes carres de deux nombres rationnels. A simple proof of the Butterfly Theorem. Ellis, Solution to Problem E, ibid.

El 1e a ete sug-geree par le Probleme 91, dont la solution apparatt a la pageet par un problemeanalogue dans Breard [1]. I wrote to Dr. His claim was demolished by Mathematiclrum in [20]. For what value of I will it be able to graze overexactly half of the field? Coxeter, Projective Geometry, Blaisdell,pp.

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## Problem 3824 from Crux Mathematicorum

Two were wrong in part a and one was wrong in part b. The resemblance of the figure to the wings of a butterfly explains the nameunder which the problem has become known. All changes of address and inquiries about subscriptions and back issues shouldbe sent to the Secretary-Treasurer of COMA: This is the trap that our lone incorrect solverfell into.

Mahoney and Leo Sauves both from Algonquin College. Soit E unsous-ensemble non vide de A, et notons EE la somme de ses elements. Zartman, Geometry, Houghton Mifflin, Boston,p. Your point regarding the doing of mathematics was important. Ellis was published in [9], but the question had alreadybeen answered by R. Then M is the midpointof PQ. Read the Text Version. Some solvershad difficulty interpreting the subtle difference between a and b.

In thatyear Berlin mathematicofum C.