MT - Business case - 300+ Mathematical Pattern Puzzles

300+ Mathematical Pattern Puzzles Number Pattern Recognition & Reasoning Chris McMullen, Ph.D. Improve Your Math Fluency Series 300+ Mathematical Pattern Puzzles Number Pattern Recognition & Reasoning Improve Your Math Fluency Series Chris McMullen, Ph.D. Copyright © 2015 Mathematics > Popular > Patterns Entertainment > Puzzles > Math Games ISBN-13: 978-1512044287 ISBN-10: 1512044288 www.chrismcmullen.com www.improveyourmathfluency.com Contents Introduction 1 Ordered 2 Patterned 3 Alternating 4 Cyclic 5 Additive & Multiplicative 6 Multiple Operations 7 Digits 8 Prime Numbers 9 Fibonacci Inspired 10 Roman Numerals 11 Powers 12 Factorials 13 Negative Numbers 14 Fractions 15 Algebraic 16 Visual 17 Arrays 18 Analogies Answers About the Author 5 9 13 17 23 29 33 39 45 49 53 59 63 71 75 85 95 101 109 117 169 Introduction Enjoy solving a variety of mathematical pattern puzzles, including prime numbers, Fibonacci-like series, visual patterns, analogies, arrays, and more. This book starts out easy with basic patterns and simple puzzles, and the level of difficulty steadily grows so that people of all ages and abilities can enjoy many of the patterns and puzzles in this book. Each chapter begins with a brief introduction (and, where necessary, a quick review) of the relevant concepts, followed by 2-3 examples of pattern puzzles with explanations. The answer, along with an explanation, to every puzzle can be found at the end of the book. Introduction Some chapters incorporate ideas from earlier chapters. For example, once prime numbers are introduced in Chapter 8 and the Fibonacci sequence is introduced in Chapter 9, these concepts may appear in a subsequent chapter. Examples Following are a few examples of the kinds of patterns that you can find in this book. Fill in the blanks. Example 1. 9, 25, 49, 81, _____, _____, _____, _____ Example 2. 15, 15, 10, 30, 30, 20, 60, 60, 40, _____, _____, _____ Example 3. Check your answers on the next page. ∞ 6 ∞ 300+ Mathematical Pattern Puzzles Answer to Example 1. Square odd numbers: 3 × 3 = 9, 5 × 5 = 25, 7 × 7 = 49, and 9 × 9 = 81. The next four numbers are 11 × 11 = 121, 13 × 13 = 169, 15 × 15 = 225, and 17 × 17 = 289. Answer to Example 2. The first 3 numbers are 15, 15, and 10. Double these to get 30, 30, and 20. Double those to get 60, 60, and 40. The next three numbers are 120, 120, and 80. Answer to Example 3. The black square advances 3 spaces clockwise along the large square: ∞ 7 ∞ 1 Ordered The patterns in Chapter 1 follow a common recognizable order, like whole numbers (1, 2, 3, 4, 5...), the alphabet (a, b, c, d, e...), or geometric shapes (triangle, square, pentagon, hexagon, heptagon...). Example 1. These even numbers progress in order, beginning with 6. 6, 8, 10, 12, 14, 16, 18... The next two numbers are 20 and 22. Example 2. These letters of the alphabet appear in order, skipping every other letter, beginning with m. m, o, q, s, u... It’s really m, skip n, o, skip p, q, skip r, s, 1 Ordered skip t, u, skip v. The next two letters are w and y (since x is skipped). Example 3. This visual pattern consists of polygons. Count the number of sides. The triangle has 3 sides, the square has 4 sides, the pentagon has 5 sides, etc. , , , , ... The next two shapes are an octagon (8 sides) and nonagon (9 sides): , #1 #2 7, ____, 11, ____, ____, 17, 19, ____ 5, ____, 15, ____, ____, 30, ____, 40 #3 _____, 600, 700, _____, 900, _____, _____, 1200 #4 25, 50, _____, _____, 125, _____, 175, _____ ∞ 10 ∞ 300+ Mathematical Pattern Puzzles #5 _____, 65, 77, _____, _____, 113, _____, 137 #6 b, d, f, ___, j, ___, ___, p #7 c, g, k, ___, s, ___ #8 _________, #9 #10 #11 , , _________, , _______, , , , _______ 15, ____, 13, ____, 11, ____, ____, 8 ____, 27, 24, 21, ____, 15, ____, ____ #12 125, _____, 115, _____, _____, 100, _____, 90 ∞ 11 ∞ 1 Ordered #13 _____, 1075, 1050, _____, _____, _____, 950, 925 #14 ___, w, v, ___, t, s, r, ___ #15 q, ___, m, ___, i, ___, e, c #16 #17 #18 y, v, ___, p, ___, ___, g, d , ________, _______, #19 #20 , , , , ________ , , , _______ A, ___, I, O, U d, f, g, h, ___, ___, l, m, n, ___, q ∞ 12 ∞