A-1 Chapter 1 RECREATIONAL MATH, PAGE 24 The boatman crosses with the goat first. Then he can take the herbs across the river. But he must return the goat temporarily so that the goat doesn’t eat the herbs. He then takes the wolf across the river. Then he returns for the goat. He will make seven crossings—four forward and three back. The answer to the St. Ives riddle is 1. SECTION 1.1, PAGE 6 13. 14. 15. 16. 32. b) To obtain the 7th triangular number, add 7 to the 6th triangular number. To obtain the 8th triangular number, add 8 to the 7th triangular number, and so on. 41. + + = + + − = n n n n n n n , 3 , 3 6, 3 6 3 2, 2 2 42. + + = + + − = n n n n n n n , 4 , 4 6, 4 6 2 2 3, 2 3 3 2 43. n n n n n n n n , 1, ( 1) 9 2 2 10 2 5, 5 5 + + + + = + = + + − = 44. + + + = + + + = + + = + + − = n n n n n n n n n n n , 5, ( 5) 2 5,2 5 11 2 16, 2 16 2 8, 8 8 SECTION 1.3, PAGE 28 48. One possible answer is below. Other answers are possible. 6 7 8 1 2 3 4 5 49. 4 3 2 5 1 6 51. 8 18 6 2 16 10 4 14 12 52. 10 3 5 11 6 7 8 9 4 57. 7 3 1 5 8 6 4 2 Other answers are possible, but 1 and 8 must appear in the center. 63. 1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4 Other answers are possible. 68. Thomas would have opened the box labeled grapes and cherries. Because all the boxes are labeled incorrectly, whichever fruit he pulls from the grapes and cherries box will be the only fruit in that box. If he pulls a grape from the box, the box must be labeled grapes; if he pulls a cherry from the box, the box must be labeled cherries. That leaves two boxes whose original labels were incorrect. Because all labels must be changed, there will be only one way for Thomas to assign the two remaining labels. REVIEW EXERCISES, PAGE 35 7. 8. 38. 21 7 8 18 10 16 15 13 14 12 11 17 9 19 20 6 39. 23 13 25 29 15 21 2717 19 42. 46. Place six coins in each pan with one coin off to the side. If it balances, the heavier coin is the one on the side. If the pan does not balance, take the six coins on the heavier side and split them into two groups of three. Select the three heavier coins and weigh two coins. If the pan balances, it is the third coin. If the pan does not balance, you can identify the heavier coin. 50. The fifth figure will be an octagon with sides of equal length. Inside the octagon will be a seven-sided figure with each side of equal length. The figure will have one antenna. 52. Some possible answers are shown. Others are possible. 4 3 12 10 8 5 1 2 6 11 7 9 1 3 11 8 12 7 4 2 5 9 10 6 4 1 12 11 7 5 2 3 8 9 6 10 CHAPTER TEST, PAGE 39 14. 40 15 20 5 25 45 30 35 10 Chapter 2 SECTION 2.1, PAGE 48 95. Answers will vary. Here are some examples. a) The set of men. The set of actors. The set of people over 12 years old. The set of people with two legs. The set of people who have been in a movie. $25 Room $ 3 Friends $ 2 Clerk $ 30 Answers
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