Dundonald wrote:

The question I have is what is the best tool to do the job? I've
borrowed a circular saw but it seems a bit like a sledge hammer to
crack a nut.

You could use your jigsaw if you break the end off a blade so that at
full stroke it is just long enough to reach through the floorboard. Then
you should be able to jigsaw along the centre line of the joist without
actually cutting the joist (much!).

(your circular saw will also do the job since you can set the depth of
cut on that to the thickness of the boards)

--
Cheers,

John.

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