Lets there are three prisoners
prisoner     bottle
1              1
2              2
3              3
1 &2      4
2&3          5
3&1          6
1&2&3   7
If poison is filled in bottle no:4 both 1 and 2 dies .
If only 1st prisoner dies the poison is in 1st bottle.
If only 2nd prisoner dies the poison is in 2nd bottle.
similarly interpret others as well
From this one can see that with 3 prisoners i can verify 7 bottles.
If you observe carefully this nothing but no of selecting 3 prisoners excluding null set.
So with 10 prisoners i can verify 1023 bottles.(1024(2^10)-1)