The CENTRE for EDUCATION in MATHEMATICS and …

The CENTRE for EDUCATION in MATHEMATICS and COMPUTING

Le CENTRE d'E?DUCATION en MATHE?MATIQUES et en INFORMATIQUE

cemc.uwaterloo.ca

2021 Results

Pascal Contest

(Grade 9)

Cayley Contest

(Grade 10)

Fermat Contest

(Grade 11)

2021 R?esultats

Concours Pascal

(9e ann?ee ? Sec. III)

Concours Cayley

(10e ann?ee ? Sec. IV)

Concours Fermat

(11e ann?ee ? Sec. V)

c 2021 Centre for Education in Mathematics and Computing

Competition Organization

Organisation du Concours

Centre for Education in Mathematics and Computing Faculty and Staff / Personnel du Concours canadien de math?ematiques

Ed Anderson Jeff Anderson Terry Bae Jacquelene Bailey Shane Bauman Jenn Brewster Ersal Cahit Diana Castan~eda Santos Sarah Chan Ashely Congi Serge D'Alessio Fiona Dunbar Mike Eden Sandy Emms Barry Ferguson Steve Furino Lucie Galinon Robert Garbary Rob Gleeson Sandy Graham

Conrad Hewitt Angie Hildebrand Carrie Knoll Wesley Korir Judith Koeller Laura Kreuzer Bev Marshman Paul McGrath Jen Nelson Ian Payne J.P. Pretti Alexandra Rideout Nick Rollick Kim Schnarr Ashley Sorensen Ian VanderBurgh Troy Vasiga Christine Vender Heather Vo Bonnie Yi

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Competition Organization

Organisation du Concours

Problems Committees / Comit?es des probl`emes

Pascal Contest / Concours Pascal

Aaron Warner (Chair / pr?esidente), St. Mildred's-Lightbourn School, Oakville, ON Melissa Hesch, University of Waterloo, Waterloo, ON Rachel Iacobucci, White Oaks S.S., Oakville, ON Hwie Lie Johns, Sutherland S.S., North Vancouver, BC Peter O'Hara, London, ON J.P. Pretti, University of Waterloo, Waterloo, ON Paule Rodrigue, Franco-Cit?e, Ottawa, ON Anna Spanik, Halifax, NS

Cayley Contest / Concours Cayley

Jen Nelson (Chair / pr?esidente), University of Waterloo, Waterloo, ON Priscilla Bengo, Don Mills C.I., Toronto, ON Rich Dlin, Toronto, ON Barry Ferguson, University of Waterloo, Waterloo, ON Carley Funk, Waterloo C.I., Waterloo, ON Ty Ghaswala, Universit?e du Qu?ebec `a Montr?eal, Montreal, QC Jordan Grant, St. John's-Kilmarnock School, Breslau, ON Christopher Ing, Vincent Massey S.S., Windsor, ON Christine Ruza, Elmira D.S.S., Elmira, ON Tim Zhou, University of Waterloo, Waterloo, ON

Fermat Contest / Concours Fermat

Paul Fennell (Chair / pr?esident), London, ON Sandra DellaMaestra, University of Toronto Schools, Toronto, ON Mike Eden, University of Waterloo, Waterloo, ON Melissa Giardina, Jean Vanier C.S.S., Milton, ON Conrad Hewitt, University of Waterloo, Waterloo, ON Steve Lau, Tara, ON Carol Miron, North Toronto C.I., Toronto, ON Martin Tuchtie, Fenelon Falls S.S., Fenelon Falls, ON

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Foreword

Avant-Propos

Our congratulations go to all who participated in this year's Pascal, Cayley and Fermat Contests. This year's Contests were great successes, with averages of 101.97, 99.19 and 97.26 across the three Contests. The number of eligible contestants with perfect papers on the three Contests were 105, 39 and 26. There was a mistake in Problem 25 on this year's Pascal Contest, and so every student was given credit for this problem. You will see that the results for this question are removed throughout this report.

As always, we would like to thank the hard-working Problems Committees. Most of the members of these Committees are active secondary school teachers from across Canada who volunteers their time and contribute dozens of hours of expertise. Without their intriguing and sometimes amusing problems, these Contests would not be possible.

We would also like to thank all participants, both teachers and students. This year's contests were written under a variety of different situations, in many cases supervised by parents and guardians who wanted to ensure that students around the world had the ability to participate despite the continuing challenges of the global pandemic. Teachers deserve extra appreciation for coordinating students both in their schools and writing remotely ? no easy task! Despite the circumstances, we hope that the papers provided you with some interesting mathematics to think about and play with. Thank you for your support! Please continue to encourage your colleagues and fellow students to become involved in our activities.

Nos f?elicitations vont `a tous les participants du Concours Pascal, Cayley et Fermat de cette ann?ee. Les Concours de cette ann?ee retentissaient de succ`es, avec des moyennes de 101,97, 99,19 et 97,26 `a travers les trois Concours. Le nombre de candidats eligibles poss?edant un concours parfait ?etait de 105, 39 et 26. Une erreur s'est gliss?ee dans le probl`eme 25 du concours Pascal de cette ann?ee. Tous les ?el`eves ont donc rec?u les points pour ce probl`eme. Vous verrez que les r?esultats pour cette question ont ?et?e supprim?es de ce rapport.

Nous aimerions surtout remercier les Comit?es de probl`emes pour leur dur travail. La plupart des membres de ces Comit?es sont des enseignant(e)s d'?ecole secondaire actifs d'un bout `a l'autre du Canada qui offre leur temps et contribuent des douzaines d'heures d'expertise. Sans leurs probl`emes perspicaces et amusants, ces Concours ne seraient pas possibles.

Nous aimerions remercier aussi tous les participants incluant les enseignants et les ?etudiants. Les concours de cette ann?ee ont ?et?e r?edig?es dans des situations tr`es diverses, souvent sous la supervision de parents, tutrices et tuteurs qui voulaient s'assurer que les ?el`eves du monde entier puissent participer malgr?e les difficult?es persistantes de la pand?emie mondiale. Les enseignantes et les enseignants m?eritent une reconnaissance particuli`ere pour avoir coordonn?e les ?el`eves `a la fois dans leurs ?ecoles et `a distance ? ce qui n'est pas une t^ache facile ! Malgr?e les circonstances, nous esp?erons que ces concours ont fourni des math?ematiques int?eressantes qui vous ont amus?es et pouss?es `a r?efl?echir. Merci pour votre soutien continu?e!

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Enrollment

Number of schools registered by province / Nombre d'?ecoles inscrit par province

AB BC MB NB NL NS NT NU ON PE QC SK YT International Total

Pascal 89 194 39 28 14 27 1 1

1083 6

49 23

1 387 1942

Cayley 41

199 28 26 13 23 1 0

924 4

45 13 1 352 1670

Fermat 40 207 28 28 14 21 1 1

1160 6 42 14 2

368 1932

Inscription

Number of students registered by province / Nombre d'?etudiants inscrit par province

AB BC MB NB NL NS NT NU ON PE QC SK YT International

Pascal 1479 2563 551 316 241 605 9 2 5561 202 1022 194 3 3773

Cayley 486

2222 318 286 183 443 8 0

4268 59

808 93 11

3679

Fermat 437 1876 299 205 151 265 4 1 4578 46 789 68 7 3851

Total

16521 12864 12577

Total number of students enrolled / Nombre d'inscriptions individuelles: 41962

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Champions ? 2021

Champions ? 2021

2021 STUDENT CHAMPIONS AND CHAMPIONSHIP TEAMS PALMARE`S INDIVIDUEL ET PALMARE`S PAR E?QUIPE 2021

PASCAL CONTEST / CONCOURS PASCAL

STUDENTS /E?LE`VES Students are listed in alphabetical order / Les ?el`eves sont nomm?es en ordre alphabetique

JAESUNG BAE KHARIS CHANG JEFFREY CHEN CAROLINE CHENG PERRY DAI ALESSANDRO DE MENECH MAX DING LEO FU RYAN FWU ANDERSON GAO DANIEL GAO MAXWELL GAO KEVIN GUO AARON HAN KEVIN HU RACHEL KANG BYURI KIM ANTON LAZARCHYK ANGELA LI GORDON LI REX LI SUNNY LI XIN CHEN LI ALLISON LIANG SUNWOO LIM DAVID LIN OU LIN ADILA LIU OWEN LIU XUEFENG LIU YUHENG LIU YINGHANG MA JUSTIN NITOI MAGGIE PANG JUHYE PARK GRACE PU LAWRENCE QIAN SRIKRISHNA RAO

School E? cole King's Christian Collegiate

Marc Garneau C.I.

A.B. Lucas S.S. White Oaks S.S.

University of Toronto Schools West Point Grey Academy Louis Riel School

University of Toronto Schools Fraser Heights S.S. Bloor C.I. Little Flower Academy

Branksome Hall

University of Toronto Schools Abbey Park H.S. Saint John H.S. Ridley College High School Marc Garneau C.I.

A.Y. Jackson S.S. Kuper Academy

Sir Winston Churchill S.S. Anderson C. and V.I. Marc Garneau C.I.

Marc Garneau C.I. R.C. Palmer S.S. St. John's-Ravenscourt School

Location Endroit Oakville, ON Calgary, AB Vancouver, BC North York, ON North York, ON London, ON Oakville, ON Richmond, BC Toronto, ON Vancouver, BC Calgary, AB Vancouver, BC Toronto, ON Surrey, BC Toronto, ON Vancouver, BC North York, ON North York, ON Toronto, ON Dundas, ON KANATA, ON Edmonton, AB Toronto, ON Oakville, ON Saint John, NB St Catharines, ON North York, ON MISSISSAUGA, ON North York, ON Kirkland, QC Surrey, BC Vancouver, BC Whitby, ON North York, ON MARKHAM, ON North York, ON Richmond, BC Winnipeg, MB

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