The Action: A theater company is conducting four two-day workshops in Lighting, Production, Rehearsals, and Staging. Your task (whether or not you choose to accept it, Mr. Phelps) is to order the four workshops over the course of five days—a sequencing game. This game has a slight twist that makes it more complex than the garden-variety sequencing game: Since each workshop lasts two days, there are actually eight entities to place (two days of Lighting, two days of Production, etc.). The Key Issues to deal with:
1) When are each of the workshops conducted?
2) Which workshops can, must, or cannot be conducted before which other workshops?
3) Which workshops can, must, or cannot be conducted after which other workshops?
4) Which workshops can, must, or cannot be conducted on the same day as which other workshops?
The Initial Setup: This game deals with days, so it makes sense to lay out the sketch like a calendar. Whenever possible, make your sketches as familiar and “real life” as possible. You’ll find the information that much more accessible. Also, remember to list the entities:
1) This rule makes the eight entities much more manageable, especially if you move it from the abstract to the particular. Put the rule into action, mentally—what does it mean? Well, if one day of the Lighting workshop is conducted on Monday, then the second day of Lighting must be conducted on Tuesday. If one day of Rehearsals is Thursday, then the other day of Rehearsals is either Wednesday or Friday. And so on. Notice that we’ve already indicated this rule in the above sketch simply by grouping the entities in twos.
2) The possibilities are further restricted with Rule 2. Each of the five days will feature at least one workshop, and each of the five days will feature no more than two workshops. This kind of restrictive rule proves very important, by providing parameters within which the game functions. Under each day, draw two dashes to represent the maximums. And again, move the rule from the abstract to the particular. What does this rule mean for the game’s action? Well, you should recognize that we essentially have 10 slots, of which 8 will be filled by workshops and thus 2 will remain empty (you can easily indicate those with X’s). Further, recognize that since every day features at least one workshop, we’ll have to have three 2-workshop days, and two 1-workshop days.
3) This rule sounds quite convoluted, but again, take a deep breath and ask yourself, what is it really saying? The phrase “begin no earlier than the day immediately following” simply means “X after Y.” So all they’re saying is, we have to insert “LL” into the sequence before we can insert “RR” or “PP.” And as with Rule 2, we should start working this out mentally, in concrete terms; here are some possibilities:
- The two earliest days for Lighting are, of course, Mon and Tues. If Lighting takes those days, then PP and RR will be inserted somehow into Wed, Thurs, and Fri (remember that all pairs are consecutive).
- If Lighting, on the other hand, takes Tues and Wed, then both PP and RR will have to completely occupy the Thurs and Fri slots . . . leaving Staging to be inserted somewhere into Mon, Tues, and Wed (remember, no more than two workshops per day).
- And that’s it for Lighting—Wed is the latest that Lighting can be scheduled, since scheduling Lighting on Thurs renders it impossible to schedule both Production and Rehearsals afterward.
Key Deductions: At this point, many of you might be moved to pick up your pencil and work out the possibilities even further. Bravo to that impulse: We’ve often said that in Step 4 of the Kaplan Method, if you can narrow down possibilities to two, or at most three, it’s usually wise to do so!
We’ve just seen that Lighting will take Mon/Tues or Tues/Wed—in short, there’s no way around it: Tuesday has to feature a Lighting workshop. That’s a must! We’ve also just seen that Rehearsals and Production can only be scheduled in Wed, Thurs, or Fri, and there are only two ways to satisfy this while keeping the two Rehearsals consecutive and the two Productions consecutive: Each must be held on either Wednesday and Thursday, or on Thursday and Friday. Therefore, Thursday’s workshops must always be Production and Rehearsals. No way around it—if Thurs is free of either Production or Rehearsals, the schedule won’t work. Build the facts we’ve just learned into the master sketch.
And what about Staging? Having added an L to Tues and indicated Thurs as “P R,” you might have noticed that Staging can only be inserted in Mon-Tues or Tues-Wed—anywhere else, and we’ll have three workshops on Thursday, a no-no. In short, Tuesday’s other workshop will have to be Staging. You may not have gotten this far with your deductions, but needless to say, all of this is huge as a basis for all of the work on this game. See how quickly the questions fall once we have the following Final Visualization down on the page:
The Final Visualization:
The Big Picture:
• Again we see how important it is to take the time, up front, to work out as much as possible about the setup. The more you know about a game before hitting the questions, the better. It takes some time to make the Tuesday and Thursday deductions, but we will see how rapidly these two deductions allow us to cruise through most of the questions.
• During Step 4 of the Kaplan Method, if you can narrow down the options to two—or at most three—it’s wise to do so. Following that impulse in this game might have led you to realize that the Tues and Thurs schedules can be ascertained fully.
• Always paraphrase the rules—rewrite them in your own, simpler words. Also, interrogate the rules. Ask “what does this mean?”; don’t be content with merely asking “what does this say?” At first glance, Rule 3 may have looked offputting. However, when you figure out what the rule means rather than what it says, it’s no different from others you’ve seen hundreds of times.
• We can’t stress this enough: Make abstract rules concrete. Activate them in your mind (and, as appropriate, with your pencil). Please study carefully how we did so with each of the three indented rules in this game. Noting in detail the ways in which we took each rule and ran it through some concrete possibilities should help you to do likewise with other rules in other games from now on.
• What principle activates everything described above? It’s the principle that the game’s action governs the game. Achieving that action—carrying it out—should always be uppermost in your mind. Example: Our job here is to schedule the workshops. If you are galvanized by that—if your every impulse is to do whatever you can to get those letters into that schedule—then you are likely to make most if not all of the realizations we discussed above. Keep asking yourself, What can I do to accomplish the action?
• Students sometimes hear a Kaplan teacher discuss a tough game in depth, and respond, “I understand it now, but how do I get all of that on my own?” Our response? Concentrate on the action of the game, and make the rules concrete. If you keep doing those two things, you will be pushing the rules toward definite “Big Deductions,” and getting the game under control.
Come back tomorrow to work on the questions for this game!