==> arithmetic/7-11.s <== The prices are: \$1.20, \$1.25, \$1.50, and \$3.16 \$7.11 is not the only number which works. Here are the first 160 such numbers, preceded by a count of distinct solutions for that price. Note that \$7.11 has a single, unique solution. 1 - \$6.44 1 - \$7.83 2 - \$9.20 3 - \$10.89 1 - \$6.51 1 - \$7.86 1 - \$9.23 1 - \$10.95 1 - \$6.60 3 - \$7.92 1 - \$9.24 2 - \$11.00 1 - \$6.63 1 - \$8.00 1 - \$9.27 1 - \$11.07 1 - \$6.65 1 - \$8.01 2 - \$9.35 1 - \$11.13 1 - \$6.72 1 - \$8.03 3 - \$9.36 1 - \$11.16 2 - \$6.75 5 - \$8.10 1 - \$9.38 1 - \$11.22 1 - \$6.78 1 - \$8.12 5 - \$9.45 2 - \$11.25 1 - \$6.80 1 - \$8.16 2 - \$9.48 2 - \$11.27 2 - \$6.84 2 - \$8.19 1 - \$9.54 1 - \$11.30 1 - \$6.86 1 - \$8.22 1 - \$9.57 1 - \$11.36 1 - \$6.89 1 - \$8.25 1 - \$9.59 1 - \$11.40 2 - \$6.93 3 - \$8.28 2 - \$9.60 2 - \$11.43 1 - \$7.02 3 - \$8.33 1 - \$9.62 2 - \$11.52 1 - \$7.05 1 - \$8.36 2 - \$9.63 2 - \$11.55 2 - \$7.07 1 - \$8.37 1 - \$9.66 2 - \$11.61 1 - \$7.08 2 - \$8.40 1 - \$9.68 1 - \$11.69 1 - \$7.11 1 - \$8.45 2 - \$9.69 1 - \$11.70 1 - \$7.13 2 - \$8.46 1 - \$9.78 1 - \$11.88 2 - \$7.14 1 - \$8.52 2 - \$9.80 1 - \$11.90 3 - \$7.20 5 - \$8.55 1 - \$9.81 1 - \$11.99 1 - \$7.25 1 - \$8.60 1 - \$9.87 1 - \$12.06 1 - \$7.26 4 - \$8.64 4 - \$9.90 1 - \$12.15 2 - \$7.28 1 - \$8.67 1 - \$9.92 1 - \$12.18 1 - \$7.29 1 - \$8.69 2 - \$9.99 1 - \$12.24 3 - \$7.35 1 - \$8.73 1 - \$10.01 1 - \$12.30 1 - \$7.37 2 - \$8.75 1 - \$10.05 1 - \$12.32 1 - \$7.47 1 - \$8.76 2 - \$10.08 1 - \$12.35 1 - \$7.50 1 - \$8.78 1 - \$10.17 2 - \$12.42 1 - \$7.52 5 - \$8.82 1 - \$10.20 1 - \$12.51 4 - \$7.56 1 - \$8.85 2 - \$10.26 1 - \$12.65 1 - \$7.62 1 - \$8.88 3 - \$10.29 2 - \$12.69 4 - \$7.65 2 - \$8.91 3 - \$10.35 1 - \$12.75 1 - \$7.67 1 - \$8.94 2 - \$10.44 1 - \$12.92 2 - \$7.70 1 - \$8.96 1 - \$10.53 1 - \$12.96 3 - \$7.74 3 - \$9.00 1 - \$10.56 1 - \$13.23 1 - \$7.77 1 - \$9.02 1 - \$10.64 1 - \$13.41 1 - \$7.79 2 - \$9.03 2 - \$10.71 1 - \$13.56 2 - \$7.80 1 - \$9.12 3 - \$10.80 1 - \$14.49 1 - \$7.82 2 - \$9.18 1 - \$10.85 1 - \$15.18 There are plenty of solutions for five summands. Here are a few: \$8.28 -- at least two solutions \$8.47 -- at least two solutions \$8.82 -- at least two solutions -- Mark Johnson mark@microunity.com (408) 734-8100 There may be many approximate solutions, for example: \$1.01, \$1.15, \$2.41, and \$2.54. These sum to \$7.11 but the product is 7.1100061.