Today’s post is in response to a student question about Logic Games:
Other than looking for variables in common, how can you find ways to get deductions from combining rules?
Of course, the easiest way to make deductions is to look at multiple rules covering the same variable or spot. But as the student asks, what about when that doesn’t happen? It doesn’t mean there’s nothing to be found. It’s often all about what takes up space.
In an ordering game, if there are multiple blocks, especially if they’re big, assess how they’ll fit together. Will they have to overlap? Will they get in each other’s way? Sometimes, this leads to a concrete deduction. But even if it doesn’t, understanding how the two blocks will have to fit together can be very helpful. See PT59, Game 4 for an example.
Some ordering games have multiple categories of variables. In this case, rules about those categories can create relationships between rules that otherwise have no explicit connection. Let’s say, for example, that there are a bunch of variables in one of those categories, and they can’t appear consecutively. That affects how the other rules will be spaced out, and how they’ll fit together. See PT 65, Game 2 and PT 68 Game 4 for examples of this.
In a grouping game, limited space in a group can lead to deductions. One of the most common deductions in grouping games goes like this: two variables can’t be in the same group, and there are only two groups (or two groups those variables are allowed to go in). One of them therefore has to go in each group, meaning that one of the spots in each group is full already. For example, suppose that out of six people – Paolo, Quebert, Rotavirus, Sharon, Thanh, and Venereal – three do crafts, and three drink. The rules tell us that Paolo and Thanh do different activities, and that Quebert and Rotavirus do the same activity. Suppose we also know that Sharon drinks. Since Paolo and Thanh do different activities, exactly one of them must do each activity, so one spot in each group is accounted for. Since Sharon drinks, that makes two spots taken out of three in the drinking group. Quebert and Rotavirus have to go together, and there’s only space for them in the crafts group. That group’s now full, so there’s only room for Venereal in the drinking group. No two rules mentioned the same variable, and yet there were tons of deductions.
This deduction also works if there are three things that can’t go together and three groups. See PT60, Game 4 and PT3, Game 3 for some good examples.
Minimum group size can also lead to deductions. If a group has to have at least a certain size, and some variables kick other variables out of a group, it’s worth taking a close look at those rules. Who are the big-time haters, and who are the small-time haters? Who doesn’t hate at all? If a big time hater is in the group, you might be forced to put in certain other variables to meet the minimum. See PT58, Game 4 for an example of this kind of deduction.
Finally, look for opportunities to do scenarios. If something big in a game is limited to two, three, or even four possibilities, it often makes sense to try out those possibilities up front, before attacking the questions. That can often lead to big deductions.
To sum it up, when the rules don’t directly combine, look for spatial restrictions. Whether it’s an ordering or a grouping game, the way the rules take up space can impact other rules and lead you to big deductions. Feel free to bring up other rule combinations you’ve noticed in the comments; the above is just a start and not a comprehensive list.