hardwood floor/nail problem

We are having our oak hardwood floors sanded and refinished . I am having the job professionally done, but there is some preparation that is my job.
Included in the preparation is being sure that any nails in the floor are either removed or countersunk into the floor far enough that they will not catch on the sander.
There are about 12 nails that have heads that are flat/round/about 6/16" in diamater. These were nailed into the floor by a previous owner in an attempt to silence squeaky floor boards. The heads are too large for normal nail set tools and in any case it seems that it would take an awful lot of force to sink these wide heads into the floor(perhaps causing damage,etc). The nails are not accessible from below.
Any suggestions about how to (a) remove the nails and/or (b) countersink the nails would be appreciated. Is it feasible to drill through the top of the nail from above thus seperating the head from the body of the nail?
Thanks in advance for your assistance,
Bob
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A good sharp Cat's Paw,
http://images.amazon.com/images/P/B00004TBQL.01.LZZZZZZZ.jpg
http://yourtools.com.ru/browse-dead-blow-hammers/good_B0001FAAAE.html
http://www.dmacc.edu/Programs/bldgtrades/images/catspaw2.jpg
or a pair of curved diagonal cutting pliers, http://www.epinions.com/Channellock_Curved_Diagonal_Cutting_Pliers_447_Shop_Tools http://www.sjdiscounttools.com/skt16108.html and a sheet of flat steel to protect the floor.

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Use a cat's paw to remove the nail. If the nail was truly stopping a squeak you still have that to contend with. Use a deck screw, countersink and plug the top.
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