 For example, when formula_99, formula_68 and formula_89, the original pile has 51 coconuts, and after three successive divisions in the night with a coconut allocated to the monkey after each division, there are 13 coconuts left over in the morning, so the final division has a coconut left over for the monkey.Other post-Williams variants which specify different remainders including positive ones (i.e.the monkey adds coconuts to the pile), have been treated in the literature.