Table for FindInstance solutions

*To*: mathgroup at smc.vnet.net*Subject*: [mg114575] Table for FindInstance solutions*From*: MH <matthewhoek at gmail.com>*Date*: Wed, 8 Dec 2010 06:41:31 -0500 (EST)

Hello. I'm trying to display in a table solutions to the equation 6S + 9N + 20T = D, where D is an integer allowed to go from 1 to 100. I can use FindInstance to find solutions with no problems. What'd I'd really like, though, is a table with four columns: one column each for D, S, N, and T. The following code gets me close to what I want, but every entry in the last three columns is the same. And, every entry gives the value for S, N, and T, instead of just the appropriate S or N or T value. For example, when D = 71, that row reads 71 {S -> 7, N -> 1, T -> 1} {S -> 7, N -> 1, T -> 1} {S -> 7, N -> 1, T -> 1}. I can interpret the correct result (7 sixes, 1 nine, and 1 twenty), but I'd like the column to read 71 7 1 1 How can I change that? Incidentally, this problem is from a current issue of Delta Airlines' Sky Magazine. The problem asks about a baker who sells donuts in boxes of 6, 9, and 20. What's the largest number of donuts you CANNOT purchase? I have the solution; I'd just like it to look a little bit nicer. :-) Thanks! MH ===== TableForm[ Table[ {D, FindInstance[ 6 S + 9 N + 20 T == D && S >= 0 && N >= 0 && T >= 0, {S, N, T}, Integers], FindInstance[ 6 S + 9 N + 20 T == D && S >= 0 && N >= 0 && T >= 0, {S, N, T}, Integers], FindInstance[ 6 S + 9 N + 20 T == D && S >= 0 && N >= 0 && T >= 0, {S, N, T}, Integers] }, {D, 1, 20, 1}], TableHeadings -> {None, {"TOTAL", "BOXES OF 6", "BOXES OF 9", "BOXES OF 20"}}, TableAlignments -> {Center}, TableSpacing -> {1, 3} ] =====