block design and group testing

Question

This is a question from course notes:

The answer I'm given is something like this:

So my questions are:

1.How do we know there should be 9 tests? why not 8 tests or 10 tests?

2.How many items are we testing? is it 9 items or 18 items? It doesn't make sense that we are doing 9 tests on 9 items.

Answer 1

The design seems to have 18 blocks and 9 varieties. The standard way to interpret this would be as 9 items and 18 tests.

Of course the dual design would have 9 blocks and 18 varieties. If you read the question carefully, it says "the items of the BIBD are the tests of the screening experiment". This suggests you want to be working with the dual.