And we have a winner!! (unless Ouabache has something else in mind)
With 4 lab animals, the number of combinations you can test are: 24
=16. The number of samples you can put into a pool are: 16/2=8 (look at the above binary columns, each column has 8 samples). This means that when your number of samples increases exponentially, the number of pools to be tested increases linearly.