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A Letter from the Editor: The Long and Winding Road 955 Scott T. Chapman Sets of Lengths 960 Alfred Geroldinger Balanced Factorizations 989 Anton A. Klyachko and Anton N. Vassilyev Cantor-Polynomials and the Fueter-Pólya Theorem 1001 Melvyn B. Nathanson Optimizing the Video Game Multi-Jump: Player Strategy, AI, and Level Design 1013 Aaron M. Broussard, Martin E. Malandro, and Abagayle Serreyn NOTES Dilated Floor Functions that Commute 1033 Jeffrey C. Lagarias, Takumi Murayama, and D. Harry Richman Quotients of Fibonacci Numbers 1039 Stephan Ramon Garcia and Florian Luca Parking Cars of Different Sizes 1045 Richard Ehrenborg and Alex Happ PROBLEMS AND SOLUTIONS 1050 BOOK REVIEW A First Course in the Calculus of Variations 1058 by Mark Kot Chris A. Marx Referee Thank You 1062 MATHBITS 959, Single Digit NFL Scores; 1049, Corrigendum to "A New Proof of the Change of Variable Theorem for the Riemann Integral" An Official Publication of the Mathematical Association of America monthly THE AMERICAN MATHEMATICAL VO LU M E 1 23, N O. 1 0 D EC E M B E R 20 1 6

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