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Problem from Hamilton Cycle Chapter: \"Four married couples met at a restaurant for dinner every Friday...

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Advance Math

Problem from Hamilton Cycle Chapter: \"Fourmarried couples met at a restaurant for dinner every Friday nightfor three weeks. Sometimes a large table was available toaccommodate all 8 people, but other times the group had to bedivided across two smaller tables each with at least 3 seats.Nobody moved to a different seat during a meal, no married coupleever sat next to one another, and no two people sat next to oneanother for more than one dinner. On the first Friday the eightpeople sat at one table.

(a) Show that the group could have sat at 2 tables with 4 seatseach for both the second and third Friday.

(b) Show that the group could have sat at 2 tables with 4 seatseach for the second Friday and at 2 tables, one with 3 seats andthe other with 5 seats, on the third Friday.

(c) Show that the group could have sat at 2 tables, one with 3seats and the other with 5 seats, for both the second and thirdFriday.

(d) Show that the group could have sat at a table for 8 for thesecond Friday and any of 3 different table combinations on thethird Friday.

Provide all working out and justification of all steps taken toreach the answer.\"

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