Hi Victoria,
That's a good question, and an interesting game. The convergence of rules in that one create a unique variable block.
Beginning with the global setup, the game provides that four sessions will be taught on days 1 through 4. With the greatest inherent numerical order, the days make a good base for the game:
Ssn:
__
__
__
__
(M,O,R,S)
Day:
1
2
3
4
Since each session involves both a nurse and a psychologist, two additional levels are required for the setup:
Psy:
__
__
__
__
(T,V,W)
Nrs:
__
__
__
__
(F,J,L)
Ssn:
__
__
__
__
(M,O,R,S)
Day:
1
2
3
4
Let's take a look at the third rule: neither F nor L will teach with T. Since there are only three nurses, and Tyler won't be teaching with Fine or Leopold, Tyler must teach with Johnson. Since T must work with J, that creates a vertical block with T and J:
T
J
The fourth rule provides that Johnson teaches session S only, creating a vertical block with J and S. If we add this to the block we have already created above, we get a vertical block that includes T, J, and S:
T
J
S
Let's now take a look at the last rule: M is taught right after S, creating an SM horizontal block. When we add this to the three variable block that we've created above, we get a large, L-shaped block that includes the variables T, J, S, and M:
T
J
S M
The second rule requires that L teach on Day 3, which forces this large L-shaped block into one of two positions: either Days 1 and 2, or Days 2 and 3:
- Psy: T .. .. ..
Nrs: J .. L ..
Ssn: S M .. ..
Day: .....1 2 3 4
OR
Psy: .. T .. ..
Nrs: .. J L ..
Ssn: .. S M ..
Day: .....1 2 3 4
With the first option, Day 2 has session M; with the second option, Day 2 has session S
And, since the two diagrams above reflect the only two options for S and M respectively, niether S nor M can ever be scheduled for Day 4. That leaves O and R as the only options for Day 4.
I hope that's helpful! Please let me know whether this is clear—thanks!
~Steve
