Tartan is right that for most people and that walking the binding around the quilt is going to be faster than doing the calculations.
Being both a math nerd and a programmer, I continued to mull on the whole question and came up with a spreadsheet that does the calculations. This allows one to calculate quickly easily where the seems will end up in any size (rectangular or square) quilt (assuming consistent intervals between the seams in the binding). If anybody would like a copy, just send me a private message with your e-mail address and I can send it to you. Amusingly, the spreadsheet shows that I made two errors in my calculations for the example (Seam 5 position is 68; Seam 9 position is 54), which illustrates that math majors are not always good at arithmetic. (In college, I like the really abstract math that didn't use numbers much - rings, groups, fields! I don't know what you do with most of that type of math - I went into the computer field after college, but boy that math is beautiful to me. Fast and accurate mental arithmetic is not my forté.)
For anybody who want to do the calculations on their own (without a spreadsheet), here is what to do.
1. Write the the number of inches between each of your seams in the binding (42 in the example
2. Write down your starting position. (40 in the example)
3. Add the number from #1 to the number from #2. (40 + 42 = 82)
Is the number greater than length current side of the quilt? (92 in the example)
If yes, then subtract the length current side of the quilt, and write that number down. (And you are now on a new side of the quilt.)
If no, then write that number down.
(So, write down the 82).
The number you wrote down is where the seam positioned.
Repeat step 3 (using the new number in place of the number from #2) as many times as you need to get back to first side and get a seam position that is greater than the starting position.
(Make sure you adjust the side length you use when you switch to a new side. Also, make sure you complete all of the fourth side and get back onto the first side - it will sorta seem like starting a fifth side as you do the calculations.)
You now have a list of all the seam positions. Look them over and see if them are within the range that you consider to be "too close" to a corner. If you've got one or more that are unacceptable, try again with a different starting position.
I expect many people eyes have glazed over (or stopped reading) well before now. It was a fun exercise for me to figure how to make the calculations and then how to describe in spreadsheet formulas and prose. Thanks for humoring me in my nerdiness.
