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logic problems:


"Logic Problems" can appear in many forms, but are all just a presentation of facts followed by a seemingly
impossible question to answer, given the limited information given. These are often referred to as "matrix
problems", requiring you to figure out a way to map the provided information onto some form of graph.

From there, you must perform a process of elimination to narrow the possible combination of facts. After each
pass through the given clues, it becomes possible to draw more and more conclusions, usually resulting in having
found all combinations of facts, including the answer to the question given.

I've found these riddles usually involve solving two challenges. First, you have to figure out how to organize
the given facts into a single "matrix" where you can mark any combination of two facts as either occurring
together or NOT occurring together. Then you have to comb over the graph and look for combinations that aren't
possible, and identify questions that rule out all possible answers except one. Certain problems don't have
an obvious way to graph them, and require some consideration to find a way to map the facts to a graph.

Once you figure out one combination of facts, you can then mark off all other possible combinations involving
those two facts. This will then allow you you further narrow down and identify additional combinations, until
you can suddenly start filling in large areas of the graph.

The second challenge usually hits when you've got your graph laid down, have filled in all the given facts,
and have made several sweeps over the graph looking for cells you can mark or eliminate. If you're not able
to solve the graph you have to go over the given clues one at a time, considering the information you've been
able to add to the graph, to gather additional information. This sometimes involves spotting careful wording
in a fact that provides a clue you overlooked, such as identifying the gender of a person, the species of a
pet, etc. I've found this to be the most challenging part of the more difficult logic problems.

Often single facts supply lots of information. Consider "the man in the blue house takes his pet out for a walk
early every morning":
- mark off all women for the blue house (since "the MAN")
- also mark off the bird and fish for the blue house (since you don't "walk" your pet bird or fish)
- an earlier fact mentioned Greg sleeps in late on Saturday, so mark off Greg for the blue house.
- you notice the remaining pets possible in the blue house are all owned by women except the great dane. You now
know who owns the great dane and the color of his house. marking those off will probably identify more facts.

If you find yourself stuck trying to solve a logic problem, it's almost always caused by your having missed
a square in the matrix that can be marked as a match OR an impossibility, or that you're not noticing some
subtle information being provided in one of the given facts. For example, in Einstein's Riddle,

Consider "The house with green walls is just to the left of the house with white walls":
Initially you might not find that useful because you don't know anything about house colors. But you CAN start
by marking the white house NOT on the far left and green house NOT on the far right. And if later you start
ruling out spots for the white house, you can refer back to this rule to mark off spots for the green house.
So it's usually necessary to go through the rules several times as more information is discovered.

Einstein's Riddle is generous, as it provides more information than the bare minimum you need, and allows you
to solve the riddle even if you over look a fact or two. Most logic problems are not so generous.


Einstein's House Riddle



last updated 12/16/2023 at 20:26:25 by make_www_index.command version 2023.12.09.A