Section 2.4

• 14. a) 5 = 9 - 3 - 1; b) 13 = 9 + 3 + 1; c) 37 = 27 + 9 + 1; d) 79 = 81 - 3 + 1.
• 16. As we saw in class, this one is a puzzler. To get you started, realize that 10 is congruent with -1 (mod 11), so 10^k is congruent with (-1)^k (mod 11). We will finish this in class.
• 18. a) 010110. b) 011111. c) 111000. d) 101100.
• 22. Look at exercises 20 and 21.
• 24. a) 2!. b) 3! + 1!. c) 3(3!) + 1!. d) 3(4!) + 2(3!) + 2! + 1!. e) 6! + 2(5!) + 4! + 2(3!) + 2(2!). f) 2(9!) + 6(8!) + 6(7!) + 2(6!) + 5(5!) + 4! + 2(3!) + 2(2!).
• 26. The carried amount is the only tricky part.
• 28. 10001100
• 32. O(n).