M. De Fonteney has remarked that, if there was an island

in the middle of the river, the passage might be always effected by the aid of a boat which could carry only two persons. If there are only two or only three couples the island is unnecessary, and the case is covered by the preceding method. His solution, involving Sn — S passages, is as follows. The first nine passages will be the same, no matter how many couples there may be : the result is to transfer one couple to the island and one couple to the second bank. The result of the next eight passages is to transfer one couple fi-om the first bank to the second bank, this series of eight operations must be repeated as often as necessary until there is left only one couple on the first bank, only one couple on the island, and all the rest on the second bank. The result of the last seven passages is to transfer all the couples to the second bank. It would however seem that if n is greater than 3, we need not require more than 6n — 7 passages from land to land.