5. The Worst-Fit bin-packing algorithm selects the bin with the most available space at each stage, generally leaving more bins with open space than the other algorithms.
6. 7*0 + 3*6 + 9*2 + 7*1 + 3*1 + 9*3 + 7*2 + 3*7 = 108, so the check digit is 8.
7. 10*0 + 9*2 + 8*1 + 7*4 + 6*8 + 5*8 + 4*2 + 3*7 + 2*2 = 175, and the next multiple of 11 is 176 = 16*11, so the check digit is 1.
8. 2*5 + 4 + 2*2 + 4 + 2*9 + 8 + 2*1 + 3 + 2*2 + 7 + 2*2 + 0 + 2*0 + 0 + 2*8 = 84. Of the odd-position digits, 3 are between 5 and 9: 84+3 = 87, so our check digit is 3.
9. 3*3 + 1 + 3*3 + 1 + 3*7 + 5 + 3*9 + 9 + 3*2 + 1 + 3*4 = 101, so the check digit should be 9. Since it is 2, the number is NOT correct.
10. 5 + 8 + 3 + 4 + 7 + 6 + 8 + 4 + 3 + 1 = 49, which has remainder 4 when divided by 9. Thus the check digit should be 4; since it is 0, the number is NOT correct.
11. 1 + 5 + 5 + 0 + 6 + 4 + 2 + 2 = 25, and the next multiple of 9 is 27. Hence the check digit should be 2; since it is, we may assume the number is correct.
12. Webster encodes to W123 using the Soundex algorithm.
13. 302 / 31 = 9 with remainder 23, so the date represents 9 complete months and 23 days, or October 23.