Need a list of combinations

Here's my situation. I'm the captain of a pool team. There are 8 members on the team and each has a skill rating of from 2 to 9. In any given match I can only play 5 players and the total of their 5 skill ratings cannot exceed 23. I would like a spreadsheet that allows me to enter the 8 different skill levels (note that these can vary from week to week) and have a spread sheet that lists all the combinations I can play that total 23 or less. Some rules:

• No player can play more than once in a match.
• All numbers are whole numbers, no decimals.
• Must play 5 players. No more. No less.

Thanks in advance for your help.

Bill

Sounds like a perfect challenge for Solver. First, install solver (options --> add-ins --> solver).

Then open attached file, open solver and hit solve.

The output you show looks like the right solution. When I run solver I get an error 53 file not found Solver DLL.

Did you install the Solver Add-in properly?

Shg's solution obviously works as well but may be a cumbersome approach when you start adding players. Solver uses linear optimization to arrive at an optimal solution.

On part of installing Solver I cannot help you any further I'm afraid, that must be a local issue. Installing the add-in works normally on all Excel versions (I've used 2003, 2007 and 2010).