Actually that’s 252 (and Céline Racicot, not 251 cauz 0 counts too: the bottle nobody touched is one combination). But if you add up all the C(10,0), C(10,1), C(10,2), C(10,2) up to C(10,10) you get 1024 just like Brett Berry. In fact it comes back to doing the same thing but in not the same order. In this method, we have no testers take of the first bottle, one different tester try the next ten, the 45 possible combinations of two testers try the next 45 bottles and so on. If we translate that to binary it makes: 0 000 000 000 and then 0 000 000 001, 0 000 000 010, 0 000 000 100… for the second step, 0 000 000 011, 0 000 000 101, 0 000 000 110 … for the third step and so on (with eleven steps total). It comes back to doing Brett Berry’s method in another order.

Tell me if I’m wrong!