You want to test for Covid-19 a large population of / individuals. You collect a sample from each and then decide to proceed as follows. You randomly divide the sample in M/k groups of k samples each. For each group, you take a small part of each of the k samples and you mix this & parts together. Then you test the mixture. If the mixture is negative it means that all & samples where negative. If the mixture is positive you must test all the k samples individually since at least one is infected. Assuming that in the population the rate of infection is 0.1, compute the expected number of test you will perform and find the optimal & to minimize the number of tests