Equal Spacing Layout
Evenly space balusters, pickets, studs, shelf pins, or layout marks in a run: N items of width w have N+1 equal gaps of (run - N x w)/(N+1) and a center-to-center pitch of gap + w. Solve for the count from a maximum gap (the smallest N with gap at or below the limit, e.g. the IRC 4-inch-sphere guard rule) or the gap from a desired count, with the mark positions (first-principles layout arithmetic).
Formula and source
N items of width w in a run R have N+1 equal gaps of gap = (R - N x w)/(N+1) and a center-to-center pitch of gap + w. Max-gap mode: smallest N with gap at or below gmax is N = ceil((R - gmax)/(w + gmax)). Item-center positions are measured from the start of the run.
Equal-spacing (baluster / picket / stud / division-point) layout - first-principles arithmetic; public domain.
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