INDEX TO VOLUME 84 AUTHORS Adam, John A., Blood Vessel Branching: Won the Bucket Game (and Lived Happily Beyond the Standard Calculus Problem, Ever After), 278-283 196-207 Hurkens, Cor A. J., see Hurkens, Antonius Alperin, Roger C. and Vladimir Drobot, JAG. Golomb Rulers, 48-55 Jakimcezuk, Rafael, The Quadratic Character Alsina, Claudi and Roger B. Nelsen, Proof of 2, 126-127 Without Words: Inequalities for Two Kayll, P. Mark, Integrals Don’t Have Numbers Whose Sum Is One, 228 Anything to Do with Discrete Math, Do Apostol, Tom M. and Mamikon A. They? 108-119 Mnatsakanian, Ellipse to Hyperbola: Keef, Patrick, see Clifton, Cody “With This String I Thee Wed” , 83-97 Kirby, Matthew and Ronald Umble, Edge Bremner, Andrew, Positively Prodigious Tessellations and Stamp Folding Puzzles, Powers or How Dudeney Done It? 120-125 283-289 Brown, Jason I., Erick Knight, and David Knight, Erick, see Brown, Jason I. Wolfe, Parity Party with Picture Proofs: An Kodokostas, Dimitrios, Letter to the Editor, Odd Checkerboard Problem, 142-149 396 Chebolu, Sunil K. and Jan Minaé, Counting Krylov, Nikolai A. and Edwin L. Rogers, Irreducible Polynomials over Finite Fields Folding Noneuclidean Strips of Paper, Using the Inclusion-Exclusion Principle, 289-294 369-371 Kubicka, Ewa and Grzegorz Kubicki, Clifton, Cody, David Guichard, and Patrick Choosing Rarity: An Exercise in Stopping Keef, How Commutative Are Direct Times, 42-48 Products of Dihedral Groups? 137-140 Kubicki, Grzegorz, see Kubicka, Ewa Daileda, Ryan C., see Olofsson, Peter Langley, Thomas, David Levitt, and Joseph Drobot, Vladimir, see Alperin, Roger C. Rower, Two Generalizations of the 5/8 Duchnowski, Matthew, Crossword Word Bound on Commutativity in Nonabelian Count, 141 Finite Groups, 128-136 Eisenberg, Bennett and Rosemary Sullivan, A Latulippe, Joe and Jennifer Switkes, “Even Modification of Sylvester’s Four Point With THAT Step Size?” ,3 77-385 Problem, 173-184 Lengvarszky, Zsolt, Convexity and Center of Farris, Frank A., The Editor’s Song, 266-267 Mass, 215-221 Fassett, Jonathon E., Eigenvalues in Filled Levitt, David, see Langley, Thomas Julia Sets, 221-227 Levrie, Paul, Stirred, Not Shaken, by Frantz, Marc, A Car Crash Solved—with a Stirling’s Formula, 208-211 Swiss Army Knife, 327-338 Livingston, H. Ryan, see Hoffman, John W. Furdui, Ovidiu, Series Involving Products of Lopez, Manuel and James Marengo, Two Harmonic Numbers, 371-377 An Upper Bound for the Expected Guichard, David, see Clifton, Cody Difference Between Order Statistics, Hodge, Jonathan K., The Mathematics of 365-369 Referendum Elections and Separable Mabry, Rick, Crosscut Convex Preferences, 268-277 Quadrilaterals, 16-25 Hoffman, John W., H. Ryan Livingston, and Marengo, James, see Lopez, Manuel Jared Ruiz, A Note on Disjoint Covering Markowsky, Greg, Pascal’s Hexagon Systems—Variations on a 2002 AIME Theorem Implies the Butterfly Theorem, Problem, 211-215 56-62 Hurkens, Antonius J. C., Cor A. J. Hurkens, Mena, Robert and Will Murray, Markov and Gerhard J. Woeginger, How Cinderella Chains for Collaboration, 3-15 Math. Mag. 84 (2011) 400-403. doi: 10.4169/math.mag.84.5.400. © Mathematical Association of America 400 INDEX TO VOLUME 84 AUTHORS Adam, John A., Blood Vessel Branching: Won the Bucket Game (and Lived Happily Beyond the Standard Calculus Problem, Ever After), 278-283 196-207 Hurkens, Cor A. J., see Hurkens, Antonius Alperin, Roger C. and Vladimir Drobot, JAG. Golomb Rulers, 48-55 Jakimcezuk, Rafael, The Quadratic Character Alsina, Claudi and Roger B. Nelsen, Proof of 2, 126-127 Without Words: Inequalities for Two Kayll, P. Mark, Integrals Don’t Have Numbers Whose Sum Is One, 228 Anything to Do with Discrete Math, Do Apostol, Tom M. and Mamikon A. They? 108-119 Mnatsakanian, Ellipse to Hyperbola: Keef, Patrick, see Clifton, Cody “With This String I Thee Wed” , 83-97 Kirby, Matthew and Ronald Umble, Edge Bremner, Andrew, Positively Prodigious Tessellations and Stamp Folding Puzzles, Powers or How Dudeney Done It? 120-125 283-289 Brown, Jason I., Erick Knight, and David Knight, Erick, see Brown, Jason I. Wolfe, Parity Party with Picture Proofs: An Kodokostas, Dimitrios, Letter to the Editor, Odd Checkerboard Problem, 142-149 396 Chebolu, Sunil K. and Jan Minaé, Counting Krylov, Nikolai A. and Edwin L. Rogers, Irreducible Polynomials over Finite Fields Folding Noneuclidean Strips of Paper, Using the Inclusion-Exclusion Principle, 289-294 369-371 Kubicka, Ewa and Grzegorz Kubicki, Clifton, Cody, David Guichard, and Patrick Choosing Rarity: An Exercise in Stopping Keef, How Commutative Are Direct Times, 42-48 Products of Dihedral Groups? 137-140 Kubicki, Grzegorz, see Kubicka, Ewa Daileda, Ryan C., see Olofsson, Peter Langley, Thomas, David Levitt, and Joseph Drobot, Vladimir, see Alperin, Roger C. Rower, Two Generalizations of the 5/8 Duchnowski, Matthew, Crossword Word Bound on Commutativity in Nonabelian Count, 141 Finite Groups, 128-136 Eisenberg, Bennett and Rosemary Sullivan, A Latulippe, Joe and Jennifer Switkes, “Even Modification of Sylvester’s Four Point With THAT Step Size?” ,3 77-385 Problem, 173-184 Lengvarszky, Zsolt, Convexity and Center of Farris, Frank A., The Editor’s Song, 266-267 Mass, 215-221 Fassett, Jonathon E., Eigenvalues in Filled Levitt, David, see Langley, Thomas Julia Sets, 221-227 Levrie, Paul, Stirred, Not Shaken, by Frantz, Marc, A Car Crash Solved—with a Stirling’s Formula, 208-211 Swiss Army Knife, 327-338 Livingston, H. Ryan, see Hoffman, John W. Furdui, Ovidiu, Series Involving Products of Lopez, Manuel and James Marengo, Two Harmonic Numbers, 371-377 An Upper Bound for the Expected Guichard, David, see Clifton, Cody Difference Between Order Statistics, Hodge, Jonathan K., The Mathematics of 365-369 Referendum Elections and Separable Mabry, Rick, Crosscut Convex Preferences, 268-277 Quadrilaterals, 16-25 Hoffman, John W., H. Ryan Livingston, and Marengo, James, see Lopez, Manuel Jared Ruiz, A Note on Disjoint Covering Markowsky, Greg, Pascal’s Hexagon Systems—Variations on a 2002 AIME Theorem Implies the Butterfly Theorem, Problem, 211-215 56-62 Hurkens, Antonius J. C., Cor A. J. Hurkens, Mena, Robert and Will Murray, Markov and Gerhard J. Woeginger, How Cinderella Chains for Collaboration, 3-15 Math. Mag. 84 (2011) 400-403. doi: 10.4169/math.mag.84.5.400. © Mathematical Association of America 400 VOL. 84, NO. 5, DECEMBER 2011 401 Miller, Steven J., Frank Morgan, Edward Scheufens, Ernst E., From Fourier Series to Newkirk, Lori Pedersen, and Deividas Rapidly Convergent Series for Zeta(3), Seferis, Isoperimetric Sets of Integers, 26-32 37-42 Schlicker, Steven J., Numbers Simultaneously Minaé, Jan, see Chebolu, Sunil K. Polygonal and Centered Polygonal, Minton, Gregory, Three Approaches to a 339-350 Sequence Problem, 33-37 Seferis, Deividas, see Miller, Steven J. Mnatsakanian, Mamikon A., see Apostol, Shirali, Shailesh A., The Bhaskara-Aryabhata Tom M. Approximation to the Sine Function, Morgan, Frank, see Miller, Steven J. 98-107 Murray, Will, see Mena, Robert Siehler, Jacob A., Depth and Symmetry in Nelsen, Roger B., see Alsina, Claudi Conway’s M,3 Puzzle, 243-256 Newkirk, Edward, see Miller, Steven J. Sullivan, Rosemary, see Eisenberg, Bennett Olofsson, Peter and Ryan C. Daileda, Switkes, Jennifer, see Latulippe, Joe Budding Yeast, Branching Processes, and Todd, Anthony, Letter to the Editor, 396 Generalized Fibonacci Numbers, 163-172 Umble, Ronald, see Kirby, Matthew Pedersen, Lori, see Miller, Steven J. Wagon, Stan, Letter to the Editor, 119 Rogers, Edwin L., see Krylov, Nikolai A. Walser, Hans R., Proof Without Words: Rosentrater, C. Roy, Representational Fibonacci Trapezoids, 295 Efficiency, 185-195 Woeginger, Gerhard J., see Hurkens, Antonius Rower, Joseph, see Langley, Thomas F€. Ruiz, Jared, see Hoffman, John W. Wolfe, David, see Brown, Jason I. Sanchez-Reyes, Javier, Letter to the Editor, Wood, William E., Squigonometry, 257-265 80 Zitarelli, David, Hilbert in Missouri, 351-364 TITLES Bhaskara-Aryabhata Approximation to the Editor’s Song, The, by Frank A. Farris, Sine Function, The, by Shailesh A. Shirali, 266-267 98-107 Eigenvalues in Filled Julia Sets, by Jonathon Blood Vessel Branching: Beyond the Standard E. Fassett, 221-227 Calculus Problem, by John A. Adam, Ellipse to Hyperbola: “With This String I 196-207 Thee Wed”, by Tom M. Apostol and Budding Yeast, Branching Processes, and Mamikon A. Mnatsakanian, 83-97 Generalized Fibonacci Numbers, by Peter “Even With THAT Step Size?” ,b y Joe Olofsson and Ryan C. Daileda, 163—172 Latulippe and Jennifer Switkes, 377-385 Car Crash Solved—with a Swiss Army Knife, Folding Noneuclidean Strips of Paper, by A, by Marc Frantz, 327-338 Nikolai A. Krylov and Edwin L. Rogers, Choosing Rarity: An Exercise in Stopping 289-294 Times, by Ewa Kubicka and Grzegorz From Fourier Series to Rapidly Convergent Kubicki, 42-48 Series for Zeta(3), by Ernst E. Scheufens, Convexity and Center of Mass, by Zsolt 26-32 Lengvarszky, 215-221 Golomb Rulers, by Roger C. Alperin and Counting Irreducible Polynomials over Finite Vladimir Drobot, 48-55 Fields Using the Inclusion-Exclusion Hilbert in Missouri, by David Zitarelli, Principle, by Sunil K. Chebolu and Jan 351-364 Minaé, 369-371 How Cinderella Won the Bucket Game (and Crosscut Convex Quadrilaterals, by Rick Lived Happily Ever After), by Antonius J. Mabry, 16-25 C. Hurkens, Cor A. J. Hurkens, and Crossword Word Count, by Matthew Gerhard J. Woeginger, 278-283 Duchnowski, 141 How Commutative Are Direct Products of Depth and Symmetry in Conway’s M,3 Dihedral Groups? by Cody Clifton, David Puzzle, by Jacob A. Siehler, 243-256 Guichard, and Patrick Keef, 137-140 Edge Tessellations and Stamp Folding Integrals Don’t Have Anything to Do with Puzzles, by Matthew Kirby and Ronald Discrete Math, Do They? by P. Mark Kayll, Umble, 283-289 108-119 402 MATHEMATICS MAGAZINE Isoperimetric Sets of Integers, by Steven J. Pascal’s Hexagon Theorem Implies the Miller, Frank Morgan, Edward Newkirk, Butterfly Theorem, by Greg Markowsky, Lori Pedersen, and Deividas Seferis, 56-62 37-42 Positively Prodigious Powers or How Letter to the Editor, by Dimitrios Kodokostas, Dudeney Done It? by Andrew Bremner, 396 120-125 Letter to the Editor, by Javier Sanchez-Reyes, Proof Without Words: Fibonacci Trapezoids, 80 by Hans R. Walser, 295 Letter to the Editor, by Anthony Todd, Proof Without Words: inequalities for Two 396 Numbers Whose Sum Is One, by Claudi Letter to the Editor, by Stan Wagon, 119 Alsina and Roger B. Nelsen, 228 Markov Chains for Collaboration, by Robert Quadratic Character of 2, The, by Rafael Mena and Will Murray, 3-15 Jakimezuk, 126-127 Mathematics of Referendum Elections and Representational Efficiency, by C. Roy Separable Preferences, The, by Jonathan Rosentrater, 185-195 K. Hodge, 268-277 Series Involving Products of Two Harmonic Modification of Sylvester’s Four Point Numbers, by Ovidiu Furdui, 371-377 Problem, A, by Bennett Eisenberg and Squigonometry, by William E. Wood, Rosemary Sullivan, 173-184 257-265 Note on Disjoint Covering Stirred, Not Shaken, by Stirling’s Formula, by Systems—Variations on a 2002 AIME Paul Levrie, 208-211 Problem, A, by John W. Hoffman, H. Ryan Three Approaches to a Sequence Problem, by Livingston, and Jared Ruiz, 211-215 Gregory Minton, 33-37 Numbers Simultaneously Polygonal and Two Generalizations of the 5/8 Bound on Centered Polygonal, by Steven J. Commutativity in Nonabelian Finite Schlicker, 339-350 Groups, by Thomas Langley, David Levitt, Parity Party with Picture Proofs: An Odd and Joseph Rower, 128-136 Checkerboard Problem, by Jason I. Upper Bound for the Expected Difference Brown, Erick Knight, and David Wolfe, Between Order Statistics, An, by Manuel 142-149 Lopez and James Marengo, 365-369 PROBLEMS The letters P, Q, and S refer to Proposals, Quickies, and Solutions, respectively; page numbers appear in parentheses. For example, P1874 (230) refers to Proposal 1874, which appears on page 230. February: P1861—1865; Q1007—1008; $1834 Bibak, Khodakhast, P1884 (387) (corrected) and $1836—1840 Bojaxhiu, Elton and Enkel Hysnelaj, $1839 April: P1866-1870; Q1009-1010; (67), $1847 (232), $1859 (391) $1841-1845 Botsko, Michael W., Q1010 (151), $1850 June: P1871—1875; Q1011-1012; (235), Q1015 (387) $1846-1850 Butler, Steve, Q1008 (64) October: P1876—1880; Qi013-1014; Calcaterra, Robert, $1843 (153), $1848 $1851-1855 (233) December: P1881—1885; Q1015—-1016; Chatadus, Stefan, $1858 (390) $1856—1860 Cheng, Eddie and Jerrold W. Grossman, $1856 (388) Abu-Saymeh, Sadi and Mowaffaq Hajja, CMC 328, $1842 (153) P1866 (150) Cowieson, Bill, $1853 (300) Alt, Arkady, $1840 (69) Diaz-Barrero, José and Pantelimon George Apostolopoulos, George, $1860 (392) Popescu, P1878 (297) Apostolopoulos, George and Omran Kouba, Deutsch, Emeric, P1861 (63) $1834 (70) Dunca, Marian, P1869 (151) Bataille, Michel, P1874 (230), Q1013 (297), Edelman, Alan and Daniel Edelman, P1877 $1857 (389) (296) VOL. 84, NO. 5, DECEMBER 2011 Edelman, Daniel and Alan Edelman, P1877 Ligouras, Panagiote, P1883 (386) (296) McMullen, Matthew, Q1011 (230) Efthimiou, Costas, $1838 (67) McPolin, Peter, $1846 (231) Falcén, Sergio and Angel Plaza, $1837 (65) Nieto, José Heber, $1854 (300) Fraiwan, Tahani and Mowaffaq Hajja, Q1012 Northwestern University Math Problem (230) Solving Group, $1841 (151) Furdui, Ovidiu, P1870 (151), Q1014 (297) OlSavsky, Gregor, P1872 (229) Goffinet, Daniel, Q1007 (64) Pérez, Felipe, $1844 (154) Goldenberg, Michael and Mark Kaplan, Perfetti, Paolo, Q1009 (151) $1841 (151) Pité, Eric, P1875 (230) Grossman, Jerrold W. and Eddie Cheng, Plaza, Angel and César Rodriguez, P1867 $1856 (388) (150) Hajja, Mowaffaq and Sadi Abu-Saymeh, Plaza, Angel and Sergio Falcon, $1837 (65) P1866 (150) Pohoata, Cosmin, P1864 (64), P1871 (229) Hajja, Mowaffaq and Tahani Fraiwan, Q1012 Popescu, Pantelimon George and José (230) Diaz-Barrero, P1878 (297) Hall, Timothy, P1882 (386) Rodriguez, César and Angel Plaza, P1867 Hetmaniok, Edyta, Roman Wituta, and (150) Damian Stfota, P1876 (296) Roelants, Herman, Q1016 (387) Hysnelaj, Enkel and Elton Bojaxhiu, $1839 Stota, Damian, Roman Wituta, and Edyta (67), $1847 (232), $1859 (391) Hetmaniok, P1876 (296) Jee, Eunsoo and Seonwoo Kim, $1855 ShahAli, H. A., P1862 (63), P1885 (387) (301) Simic, Slavko, P1881 (386) Just, Erwin, P1865 (64) Simons, John L., $1851 (298) Kaplan, Mark and Michael Goldenberg, Stenger, Allen, $1845 (155) $1841 (151) Stephens, Richard, P1880 (297) Kim, Seonwoo and Eunsoo Jee, $1855 Sung, Wong Fook, P1879 (297) (301) Thong, Duong Viet, P1863 (64) Knuth, Donald E., P1868 (150) Tomper, Bob, $1836 (65) Kouba, Omran, $1849 (234) Trif, Tiberiu, $1838 (66) Kouba, Omran and George Apostolopoulos, Wituta, Roman, Edyta Hetmaniok, and $1834 (70) Damian Stota, P1876 (296) Lampakis, Elias, P1873 (229) Zhou, Li, $1852 (299)