My secondary school, CRGS, admits (or used to admit–I’m not sure now) 100 people each year (technically, 96+4). They are to be split into *h* = 4 houses, such that the houses have equal numbers and siblings are in the same house as each other. What happens if they have a year of fifty pairs of twins, or twenty-five sets of quadruplets?

(I believe there’s also a condition on how the four houses should be distributed evenly across the forms, but for simplicity let us ignore it.)

**More serious question:** Let us call an intake *unresolvable* if the two conditions cannot be satisfied. For a given probability distribution of twins, triplets, *etc.*, consider the probability P(*n*) that an intake of *h**n* people will be unresolvable. What values of *n* are local minima of P(*n*)?