Any mathematicians out there?

[Parlo]

With odd numbers of holes, one is always in the centre.
If the bar had a full radius on each end, then the end holes would be in the centre of the radius. The distance would be 1/2 the material width in from the end, I would also use this distance if the bar had square ends.

 

[Winegrower]

This is what high school algebra ought to teach us, and does, if one listens. Seems like I have a problem like this come up frequently enough (holes in a bar, pickets in a fence, spacers in a drawer, etc.) that I use this, but I draw a sketch and write down the equation each time:

Let X equal the distance at the end of the bar to the first hole, H equal the number of holes, D the distance between holes, and L equal the length of the bar. Then,

2X + (H-1)D = L

or solving for D,

D = (L-2X)/(H-1)

Nobody would remember this formula, but it's easy to construct the equation on the spot for whatever problem situation you have.

 

[Jake M]

.... and more importantly how did you figure it out.....

You've got good advice and formulas here. I can't improve on that, but I can give you a little insight that really was an epiphany for me.

In your case, you're working with center points on a bar. The same thing goes for lines on a tape measure, graduations on a machine dial, holes in a cribbage board, or cutting up a random scrap of two by four into temporary blocking of who cares what length, you just want them about equal.... You're not counting center points, you're not counting lines, you're not counting holes, and you're not counting cuts. They're nothing to you. You're counting SPACES.

No, it's not gonna change your life, and if you do something crazy like you want to equally place those three holes, but you want to define independantly how far from the end of the bar each "end hole" will be, you still might have to draw a picture on the back of an envelope... but it will help you pick from the myriad of equations you already know (or could come up with right on the spot). For example, three holes, intuition would tell you that the equation is: spacing= x/3. But it's not. If you count spaces... the equation is very intuitive as: spacing = x/4

 

[whitmore]

There's a specification ambiguity here. Is 'space' from bar edge to hole center and hole center to
hole center, or is it bar edge to hole edge and hole edge to hole edge?
There's also some leeway in the '10 inch' measurement, which might sometimes
mean 10.000" +/-.001".

If it means the difference in getting paid or not, you attend these details before making chips.

 

[Lo-Fi]

I do stuff like this in CAD all the time. As long as I feed in the correct figures, calculation errors are impossible. Then there's the possibility of spitting out a pdf to print actual size, spray adhesive to the work, punch and go at it. Heck of a lot quicker than scribing!