1.3 Problem-Solving Procedures 33 55. Dominos Consider a domino with six dots as shown. Two ways of connecting the three dots on the left with the three dots on the right are illustrated. Using three lines, in how many ways can the three dots on the left be connected with the three dots on the right? 6 ways 56. Stack of Cubes Identical cubes are stacked in the corner of a room as shown. How many of the cubes are not visible? 20 cubes 57. Consecutive Digits Place the digits 1 through 8 in the eight boxes so that each digit is used exactly once and no two consecutive digits touch horizontally, vertically, or diagonally. * 58. Handshakes All Around Five salespeople gather for a sales meeting. How many handshakes will each person make if each must shake hands with each of the four others? 4 Challenge Problems/Group Activities 59. Income Taxes Following is the federal income tax rate schedule for a person filing a single return in 2023. 48. Tracing a Figure Try to retrace the figure without lifting your pencil from the paper or retracing a line. It can be done, but you need to begin at certain locations. We will discuss problems of this type in Chapter 13. * 49. Numbers in Circles Place the numbers 1 through 6 in the following circles so that the sum along each of the three straight lines is the same. Each number must be used exactly once. (Note: There is more than one correct answer.) * 50. Cuts in Cheese If you make the three complete cuts in the cheese as shown, how many pieces of cheese will you have? Eight pieces 51. Magic Square Create a magic square by using the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 18. The sum of the numbers in every column, row, and diagonal must be 30. * 52. Magic Square Create a magic square by using the numbers 3, 4, 5, 6, 7, 8, 9, 10, and 11. The sum of the numbers in every column, row, and diagonal must be 21. * In Exercises 53–55, use the three magic squares illustrated to obtain the answers. 8 3 6 7 4 1 9 2 5 10 15 14 7 8 9 13 12 11 3 8 7 0 1 2 6 5 4 53. Magic Square Examine the 3 by 3 magic squares and determine the sum of the four corner entries of each magic square. How can you determine the sum by using a key number in the magic square? The sum of the four corners is 4 times the number in the center. 54. Magic Square For a 3 by 3 magic square, how can you determine the sum of all the numbers in the square by using a key value in the magic square? Multiply the center number by 9. *See Instructor Answer Appendix Taxable Income Taxes $0 $11,000 − 10% of taxable income $11,001 $44,725 − $1100 12% + of the amount over $11,000 $44,726 $95,375 − $5147 22% + of the amount over $44,725 $95,376 $182,100 − $16,290 24% + of the amount over $95,375 $182,101 $231,250 − $37,104 32% + of the amount over $182,100 $231,251 $578,125 − $52,832 35% + of the amount over $231,250 $578,126 or more $174,238.25 37% + of the amount over $578,125 Source: IRS.gov a) Horace works as a waiter and earned $10,256 in taxable income in 2023. Determine the federal income taxes Horace must pay. $1025.60 b) Shelby works as an auto mechanic and earned $63,478 in taxable income in 2023. Determine the federal income taxes Shelby must pay. $9272.66
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