**MSRI Mathematical Circles Library**

Volume: 15;
2014;
376 pp;
Softcover

MSC: Primary 00; 97; 51; 05; 12;

**Print ISBN: 978-1-4704-1880-9
Product Code: MCL/15**

List Price: $45.00

AMS Member Price: $36.00

MAA Member Price: $40.50

**Electronic ISBN: 978-1-4704-1997-4
Product Code: MCL/15.E**

List Price: $45.00

AMS Member Price: $36.00

MAA Member Price: $40.50

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#### Supplemental Materials

# The ARML Power Contest

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*Thomas Kilkelly*

A co-publication of the AMS and the Mathematical Sciences Research Institute

The ARML (American Regions Math League) Power Contest is truly a
unique competition in which a team of students is judged on its
ability to discover a pattern, express the pattern in precise
mathematical language, and provide a logical proof of its
conjectures. Just as a team of students can be self-directed to solve
each problem set, a teacher, math team coach, or math circle leader
could take these ideas and questions and lead students into problem
solving and mathematical discovery.

This book contains thirty-seven interesting and engaging problem
sets from the ARML Power Contests from 1994 to 2013. They are
generally extensions of the high school mathematics classroom and
often connect two remote areas of mathematics. Additionally, they
provide meaningful problem situations for both the novice and the
veteran mathlete.

Thomas Kilkelly has been a mathematics teacher for forty-three
years. During that time he has been awarded several teaching honors
and has coached many math teams to state and national
championships. He has always been an advocate for more discovery,
integration, and problem solving in the mathematics classroom.

In the interest of fostering a greater awareness and appreciation of
mathematics and its connections to other disciplines and everyday life, MSRI
and the AMS are publishing books in the Mathematical Circles Library series as
a service to young people, their parents and teachers, and the mathematics
profession.

Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).

#### Readership

Undergraduates, graduate students, and research mathematicians interested in high school mathematics.

#### Table of Contents

# Table of Contents

## The ARML Power Contest

- Cover Cover11
- Title page iii4
- Copyright page iv5
- Contents v6
- Preface xi12
- Color transformations 116
- Induction 722
- Rook polynomials 1530
- Rotating decimals 2136
- Regular closed linkages 2742
- Factorial polynomials 3752
- Integer geometry 4560
- Unit fractions 5368
- Chromatic polynomials 6176
- Twenty-five point affine geometry 6984
- Square-sum partitions 7792
- Slides, rolls, and rolides 8398
- Pythagorean triples 91106
- Cevians 99114
- Insane tic-tac-toe 111126
- Three addition problems 123138
- Number theoretic functions 141156
- Errors in mathematical reasoning 151166
- Mathematical strings 159174
- Right triangular inscribings 169184
- Algebra of electrical circuitry 181196
- Triangular trigonometry 199214
- Electing a candidate 211226
- Three’s a charm! 219234
- The stretch method 227242
- Random walks in trees 237252
- Mathematical billiards 247262
- The game of Yahtzee 257272
- Basimal fractions 265280
- Slitherlinks 275290
- Drawing ellipses 293308
- Deltorials 309324
- A geometry with straight and curved lines 319334
- Number puzzles 327342
- The power(s) of Fibonacci 339354
- Brahmagupta’s cyclic quadrilaterals 349364
- Rational trigonometry 367382
- Back Cover Back Cover1393