Mice and cages experimental design
An experimental design is studied where mice should be placed into cages according to two different constraint settings. In the first one, mice are placed in contiguous cages with the constraint of changing cage at each day t, avoiding neighbours of days t 1 and t + 1 and meeting in the end all other mice. In the second setting, an additional constraint compels mice to change side at each step so that one half of the mice meets only the other half. A method is presented for the first setting and two for the second one, one of the latter taking advantage of finite fields in a simple and very similar way to what happens when dealing with mutually orthogonal latin squares.