Chris Lane, the head professional at Royal Oak Country club, must develop a sche
ID: 3246877 • Letter: C
Question
Chris Lane, the head professional at Royal Oak Country club, must develop a schedule of matches for the couples' golf league that begins its season at 4PM tomorrow. Eighteen couples signed up for the league and each couple must play every other couple over the course of the 17 week schedule. A possible complication is that one of the couples told Chris that they may have to cancel for the season. They told Chris they would let him know by 1PM tomorrow whether they will be able to play this season. Prepare a report for Chris Lane. Your report should include, at minimum, the following items:
-A schedule that will enable each of the 18 couples to play every other couple over the 17 week season
-A contingency schedule that can be used if the couple that contacted Chris decides to cancel for the season.
Please provide formula used for creating scedule.
Explanation / Answer
(A)
Given that, 18 couples to play every other couple over the 17 week season, so break the 18 couples up into 3 groups. The first six couples in the first group can then be identified as T1, T2, T3, T4, T5, T6; the second six couples in the second group can be identified as T7, T8,…, T12; and the last six couples in the third group can be identified as T13, T14,…, T18. We begin by developing a schedule for the first 5 weeks of the season so that each couple plays every other couple in its own group. This can be done easily by trial and error.
Then, develop the schedule for the next 3 weeks (6th, 7th and 8th week), we create 3 new six-couple groups by pairing 3 of the teams in each group with 3 of the teams in another group; i.e., (T1, T2, T3, T7, T8, T9), (T13, T14, T15, T4, T5, T6), and (T10, T11, T12, T16, T17, T18). Within each of these new groups, matches can be scheduled for 3 weeks without any couples playing a couple they have played before.
Similarly, the final 9 weeks, we continue to create new groups by pairing 3 teams from the original groups with 3 teams from the other groups that they have not yet been paired with. Then a 3-week schedule is developed as above. Shown below is a set of groups for the next 9 weeks.
Weeks 9-11
(T1, T2, T3, T10, T11, T12) (T7, T8, T9, T13, T14, T15) (T4, T5, T6, T16, T17, T18)
Weeks 12-14
(T1, T2, T3, T13, T14, T15) (T7, T8, T9, T16, T17, T18) (T10, T11, T12, T4, T5, T6)
Weeks 15-17
(T1, T2, T3, T16, T17, T18) (T7, T8, T9, T4, T5, T6) (T10, T11, T12, T13, T14, T15)
Thus, the scheduling chart as per above said process :
Team playing with
Week
W1
W2
W3
W4
W5
W6
W7
W8
W9
W10
W11
W12
W13
W14
W15
W16
W17
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T2
T5
T6
T4
T3
T8
T9
T7
T11
T12
T10
T14
T15
T13
T17
T18
T16
T3
T4
T5
T6
T9
T7
T8
T12
T10
T11
T15
T13
T14
T18
T16
T17
T4
T6
T5
T16
T17
T18
T5
T6
T17
T18
T16
T6
T18
T16
T17
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T4
T5
T6
T8
T11
T12
T10
T9
T14
T15
T13
T17
T18
T16
T5
T6
T4
T9
T10
T11
T12
T15
T13
T14
T18
T16
T17
T6
T4
T5
T10
T12
T11
T16
T17
T18
T4
T5
T6
T13
T14
T15
T11
T12
T17
T18
T16
T5
T6
T4
T14
T15
T13
T12
T18
T16
T17
T6
T4
T5
T15
T13
T14
T13
T14
T15
T16
T17
T18
T4
T5
T6
T14
T17
T18
T16
T15
T5
T6
T4
T15
T16
T17
T18
T6
T4
T5
T16
T18
T17
T17
T18
T18
(B)
If one of the couples should cancel, the schedule can be modified easily. Designate the couple that cancels, say T10, as the Bye couple. Then whichever couple is scheduled to play couple T10 will receive a Bye in that week. With only 17 couples a Bye must be scheduled for one team each week.
Team playing with
Week
W1
W2
W3
W4
W5
W6
W7
W8
W9
W10
W11
W12
W13
W14
W15
W16
W17
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T2
T5
T6
T4
T3
T8
T9
T7
T11
T12
T10
T14
T15
T13
T17
T18
T16
T3
T4
T5
T6
T9
T7
T8
T12
T10
T11
T15
T13
T14
T18
T16
T17
T4
T6
T5
T16
T17
T18
T5
T6
T17
T18
T16
T6
T18
T16
T17
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T4
T5
T6
T8
T11
T12
T10
T9
T14
T15
T13
T17
T18
T16
T5
T6
T4
T9
T10
T11
T12
T15
T13
T14
T18
T16
T17
T6
T4
T5
T10
T12
T11
T16
T17
T18
T4
T5
T6
T13
T14
T15
T11
T12
T17
T18
T16
T5
T6
T4
T14
T15
T13
T12
T18
T16
T17
T6
T4
T5
T15
T13
T14
T13
T14
T15
T16
T17
T18
T4
T5
T6
T14
T17
T18
T16
T15
T5
T6
T4
T15
T16
T17
T18
T6
T4
T5
T16
T18
T17
T17
T18
T18
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