problem from hamilton cycle chapter: four married couples met at a restaurant for dinner every friday night for three weeks. sometimes a large table was available to accommodate all 8 people, but other times the group had to be divided across two smaller tables each with at least 3 seats. nobody moved to a different seat during a meal, no married couple ever sat next to one another, and no two people sat next to one another for more than one dinner. on the first friday the eight people sat at one table.
(a) show that the group could have sat at 2 tables with 4 seats each for both the second and third friday.
(b) show that the group could have sat at 2 tables with 4 seats each for the second friday and at 2 tables, one with 3 seats and the other with 5 seats, on the third friday.
(c) show that the group could have sat at 2 tables, one with 3 seats and the other with 5 seats, for both the second and third friday.
(d) show that the group could have sat at a table for 8 for the second friday and any of 3 different table combinations on the third friday. explicitly show the ways in which they could have sat at the table for all 3 different table combinations on the third friday.