A Harder PuzzleNext Things Next

Now for a slightly more elaborate example. Have a look at the puzzle of the Inconsequential Seminars .

Again the problem is to match up people against dates, venues and subjects. The basic idea is the same as in the Four Spies problem, but this time there are five things of each sort rather than four, and four sorts rather than three. Hence the puzzle is more complex.

After trawling through the puzzle description, we can isolate the list of professors: Dodder, Plodder, Madder, Lupi and Scatter. The months, of course, you know. The venues are the departments of: Trivia, Logic-Chopping, Nitpicking, Footling and Minor Matters. The five titles, in no particular order, are:

• A Hundred Years of Inconsequentialism (Keynote Address)
• The Concept of Lunch in Early Schopenhauer
• Vagueness Revisited
• How To Put Things On Top Of Other Things
• String Lengths: A Comparative Study

For conciseness, the department names and (especially) the talk titles should be abbreviated. All four sorts (months, professors, departments, titles) can be given as enumerated sorts, though only in the case of the months does the order within the enumeration matter.

On the right is my suggested formulation. If you don’t like it, you can edit it as much as you like. After each edit, re-run the solver to make sure you still get the same solution!

We want the solver to determine three functions, assigning to each month the speaker, the venue and the topic. There is nothing magic about picking “months” as the starting point: any representation of the four-way mapping will do. Of course, all three functions are one-to-one mappings between the respective sorts.

Again, most of the constraints are quite straightforward. If you followed the ones for the Four Spies, you should be able to read these. The only constraint that really requires comment at this point is the one saying that Professor Madder speaks in the month immediately before the talk on vagueness:

ALL x (speaker(x)=Madder IMP topic(x+1)=Vagueness).

Note the keyword IMP for saying that one statement implies another: if the speaker in month x is Madder, then the topic in month x+1 is vagueness. Note also that month x+1 is the month after x (adding one to a month gives you the next month). Note also that in the case where x is the last month (May) month x+1 does not exist! In that case, it so happens that the constraint comes out true anyway, for the vacuous reason that May’s speaker is not Professor Madder, but in general you will need to take care over things like that, because strange effects tend to happen when some term like “x+1” takes you off the map.