# HW5.docx - HW 5 Exercise 6.5.1: Proving divisibility...

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HW 5Exercise 6.5.1: Proving divisibility results by induction (b).b. Prove that for any positive integer n, 6 evenly divides 7n- 1.Exercise 6.6.1: Proofs by strong induction - combining stamps (b). Note: You have to usestrong induction here. You will lose points if you use regular induction.b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-centstamps.Exercise 6.7.1: Proving the correctness of while loops using loop invariants (b).b.Exercise 7.1.2: Counting passwords made up of letters, digits, and special characters (a),(b), (c).Digits = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } = 10Letters = { a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z } = 26Special characters = { *, &, \$, # } = 4Total char = 40a.string of length 6 = 406=406b. String of length 7 = 407String of length 8 =408String of length 9 = 409=407+ 408+ 409c.total char = 40character = 26= 14 with no characters=14(406+ 407+ 408)Exercise 7.1.4: Dividing up a print job (a), (b), (c).100-page document4 printersa. 100 pages assigned to 4 printers =4100b. first and last color pages, 2 printers print color/bw= 4 * 498c. 25 assigned to same printer= 44Exercise 7.2.2: Using the bijection rule to count palindromes (c).

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Natural number, ASCII, Don