Hmmm... 2nd time posting this... maybe it'll work this time.

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x K
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HW floor boards run vertical
--- Joists, 2x10, 16" OC, 15' span
x cross braces (a couple of anbled 2x4s)
K 35lb kid bouncing here
S shakes the floor here

A coworker is convinced that the cross bracing is not adequate and
suggested additional blocking

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Looks simple enough. I might try it since it won't be that difficult
or costly.
Should I...

Use 2x10s (same as the joists) or can I use other scrap lumber?
plywood?
notch out for pipes/electrical?
nail or screw? I'm leaning towards a round head framing nailer.