Which one of the following could be the list of the students who work the second shifts at the gallery, in order from...

Irina on January 8, 2020

@mamie,

There is no hard and fast rule. The more restrictive the rules are, the more likely you'll be able to write out all the scenarios during the setup. The more open-ended the game is, the less beneficial it is to write out all the scenarios. This specific game could go either way, it is definitely quicker to go through the questions with three scenarios though.


Five students - G H J K L work during an exhibit that runs M through F. Each day has two shifts with each student working exactly two shifts. Each shift is worked by exactly one student.
This means we have 10 shifts overall, 2 shifts per day over 5 days.

1 ___ ___ ___ ___ ___
2 ___ ___ ___ ___ ___
M T W Th F

The following rules apply:

(1) No student works both shifts of any day.

This rule is fairly self-explanatory, if a student works a shift on one day, his other shift must be on a different day.

(2) On two consecutive days, L works the second shift.

This rule tells us that L only works the second shift and there is LL block somewhere in the second shift schedule.

(3) On two nonconsecutive days, G works the first shift.

This rule tells us that G works only the first shift but his days cannot be consecutive.

1 ___ ___ ___ ___ ___ G _ G
2 ___ ___ ___ ___ ___ LL
M T W Th F

(4) K works on T & F

1 ___ ___ ___ ___ ___ G _ G
2 ___ ___ ___ ___ ___ LL
M T W Th F
K K

(5) H and J work on the same day as each other at least once.

This rule tells us there is at least one HJ combination on one of the days though this rule does not exclude the possibility of two days where H & J work together. Since we know that K works on T &F, HJ combination must be on either M, W, or Th.

(6) G & L never work the same day as each other.
Since G & L work different shifts, this rule tells us that L & G shifts fall on four different days.
This rule also allows us to infer that if HJ work on W, then LL would have to either go on MT or ThF. This makes it impossible for G G to work two non-consecutive days and not work on the same day as L. Hence, HJ must go on M or Th.

1 ___ ___ H ___ ___ G _ G
2 L L J ___ ___
M T W Th F
K K

We can combine all the inferences into the final diagram:

1 ___ ___ ___ ___ ___ G _ G
2 ___ ___ ___ ___ ___ LL
M T W Th F
/HJ K /HJ K

Now, we could try a couple of different scenarios given how restrictive the placement of HJ is.

1. HJ/JH on M

If HJ is on M, we can only have LL block on WTh, otherwise, it is impossible to have G work two consecutive days and avoid working on the same days as L. GG then goes on T & F, and we already know that K works on T & F and she must work the second shift since G only works the first shift. The remaining 1st shift on W & Th could be filled with either H or J.

1 H/J G /H/J /H/J G
2 H/J K L L K
M T W Th F


2. HJ/ JH on Th

If HJ is on Th, we could only have LL block on MT or TW as these are the only consecutive days with open shifts.

(a) option 1 - LL on MT

If LL works the second shift on MT, then G must work the first shift on W and F. K must work the first shift on T and the second shift on F. The remaining shifts could be filled by either J/F.

1 /H/J K G J/H G
2 L L J/H J/H K
M T W Th F

(b) option 2 LL on TW

If LL works the second shift on TW, then G must work the first shift on M and F. K must work the first shift on T and the second shift on F. The remaining shifts could be filled by either J/F

1 G K H/J J/H G
2 H/J L L J/H K
M T W Th F

It is possible to go through this game without writing out these three scenarios as well, it is a matter of personal preference. If you could come up with all the scenarios fairly quickly, it is certainly helpful, but I would not spend too much time on them as long as you have all the other rules diagrammed.

Let me know if you have any other questions.