How To Solve Logic Puzzles
If
you’ve never solved a logic puzzle before, this introduction will show you
how. We’ll go step by step
through two simple puzzles, and give you some solving tips along the way.
A
logic puzzle is a test of your ability to think clearly.
Usually you’re asked to match up sets of things.
For example, you might be told that four men each own an exotic pet, and
to solve the puzzle you’d match up each man’s first name with his last name
and his kind of pet. You figure out
how to match them up by studying a lits of clues, like “The llama doesn’t
belong to Duane.”
To
make solving easier, puzzlers like to use a solving grid to record data
they’ve deduced. Seeing the
information neatly organized in black and white helps them make further
deductions.
There
are two kinds of solving grids: the
“crosshatch” grid and the “fill-in” grid.
sometimes you can’t tell which kind will work best until you’ve spent
a lot of time trying to solve the puzzle with the wrong kind.
We will try to provide the grid that is most useful to the solver.
We’ll provide you both kinds if we think it will help.
Let’s
look at a typical puzzle that works best with a crosshatch grid.
Pet
Owners
Each
of four men owns a different species of exotic pet. From the following clues, can you figure out each man’s
full name and what kind of pet he owns?
Here’s
the crosshatch grid:
Let’s
look first at Clue 1. From it we
can see that Abner isn’t Mr. Engels or Mr. Foster.
We record this information in the solving grid by putting an x (meaning
“n”) in the square at the intersection of “Abner” and “Engels,” and
another x at the intersection of “Abner” and “Foster.”
Now
let’s look at Clue 5. From it we
learn that Abner doesn’t own the king cobra, and that Abner isn’t Mr.
Gunter. Put x’s in the
intersections of “Abner” and “Gunter,” and “Abner” and “King
cobra.”
If
you were careless, you might without thinking put an x into the intersection of
“Gunter” and “King cobra.” Does
Mr. Gunter own the king cobra? Well,
maybe he does and maybe he doesn’t, but clue 5 really doesn’t say anything
about it. Read each clue carefully
and think about what it’s really saying; if you jump to a wrong conclusion
now, you’ll be confused later on.
New
we can see at a glance that Abner isn’t Mr. Engels, Mr. Foster, or Mr. Gunter.
We can make a deduction: Abner must be Mr. Halevy.
We’ll put a large dot (meaning “yes”) in the intersection of
“Abner” and “Halevy.” And
that means we can also put x’s in the intersections of “Halevy” and
“Bruce,” “Chuck,” and “Duane.”
Whenever you add a dot to the grid, be sure to add any x’s you can;
they’ll often lead to more deductions.
That
was a fairly simple deduction, but in order to solve this puzzle you’ll need
to make some deductions that are a little trickier. Go through the rest of the clues and put x’s into the grid
wherever you can. You’ll end up
with this:
Sometimes,
with a very easy puzzle, just putting the information in the grid is enough to
make the solution fall out to you. This
puzzle’s a bit harder, though, and at first glance there doesn’t seem to be
enough information to make any more deductions.
But the information is there; you just have to work with it a little.
Take a pencil and fill in the rest of the grid yourself as you read on.
Mr.
Halevy doesn’t own the iguana. Since
Abner is Mr. Halevy, that means Abner doesn’t own the iguana either, right?
Put an x in the intersection of “Abner” and “Iguana”
and you’re ready to make another deduction: the iguana is owned by
Bruce. Add the appropriate dot and
x’s to the grid. (Transferring
information from one section of the grid to another, as you just did, is an
important step in solving, and it’s an easy one to overlook.)
Bruce
isn’t Mr. Foster, so Mr. Foster doesn’t own the iguana.
Voila! Another deduction:
Mr. Foster owns the llama.
Mr.
Foster is either Chuck or Duane,
while the llama's owner is either
Abner or
Chuck. Since both are the same man,
it must be Chuck who is Mr.
Foster and owns
the llama.
Now
Abner Halevy's pet can only be the
jackal, and Duane's pet, by elimination, must be the king cobra.
Don't forget to
add a dot at the intersection of
"Halevy" and
"Jackal," and the x's that go
with it.
And now you seem to be stuck. Bruce owns the iguana, and Duane owns the king cobra, but you can't tell from the grid which one is Mr. Engels and which one is Mr. Gunter. Is there anything in the clues you've missed? Why, yes: Mr. Engels' pet is named Sparky (clue 1), while Duane's pet is named Waggles (clue 4), so Duane can't be Mr. Engels. As you solve logic puzzles, you'll learn that you often need to combine facts from two or more clues to make a deduction.
So
here’ your final solution: Bruce
Engels owns the iguana, Chuck
Foster owns
the llama, Duane Gunter owns the
king cobra, and Abner Halevy owns
the jackal.
At
this point you know enough to solve
most of the puzzles that have
crosshatch grids.
Now
let’s look at a similar puzzle where a crosshatch grid doesn’t work very
well.
More Pet Owners
Doris and three other women each own a different species of exotic pet. From the following clues, can you figure out each woman's full name (one is Ms. Hanker) and what kind of pet she owns (one owns a kangaroo)?
1. All four—Alice, Ms. Esping, Ms. Florin, and the ibex's owner—belong to a club for owners of unusual pets.
2. The leopard doesn't belong to Bette.
3. The jaguar doesn't belong to Alice.
4. Ms. Glover, who doesn't own the leopard, lives next door to Chloe.
5. Bette, who isn't Ms. Florin, doesn't own the ibex.
6. Ms. Esping doesn't own the jaguar.
And
here’s the fill-in grid:
It doesn't look as helpful as the cross-hatch grid, does it? And yet we'll see that the puzzle practically solves itself on a fill-in grid, while if you tried to use a crosshatch grid for this puzzle, you'd just get this far and no farther:
Here’s
A Hot Tip
Very often, the way to to break into a puzzle that has a fill-in grid is
to find a list of all the people involved. There's one in clue 1, so we start by
putting each woman named in clue 1 into a different column of the grid:
Fill in the rest of the grid yourself as you read on. The jaguar doesn't belong to Alice (clue 3) or Ms. Esping (clue 6), so by looking at our grid we can see it must belong to Ms. Florin.
Bette is neither Ms. Florin nor the ibex's owner (clue 5), so she must be Ms. Esping.
The leopard doesn't belong to Bette Esping (clue 2), so it belongs to Alice, and by elimination the kangaroo belongs to Bette Esping.
Alice, who owns the leopard, isn't Ms. Glover (clue 4), so she is Ms. Hanker, and Ms. Glover is the ibex's owner. Ms. Glover isn't Chloe (clue 4), so she is Doris, and Chloe is Ms. Florin.
And there's your answer: Bette Esping owns the kangaroo, Chloe Florin owns the jaguar, Doris Glover owns the ibex, and Alice Hanker owns the leopard.
More
Solving Tips
Read a puzzle's introduction carefully,
and make sure you understand what you're trying to figure out. If each
person has two pets, for example, and you assume each person has only one,
you'll end up in a muddle!
Information
you’ll need to solve the puzzle is often contained in the introduction.
For example, the introduction to a puzzle about the seating chart at a
dinner party might tell you that no husband was seated next to his own wife.
Don't miss those important clues.
Stuck? Then go
over the clues again, one at a time. Have you really used every bit of
information that can be squeezed out of each one?
Another way to
get unstuck — though it's more work — is to make an assumption. Assume,
say, that Alfred is Mr. Greene, and see where that leads. (Make up a second
solving grid on a piece of scratch paper for this. Then if your assumption
turns out to be wrong, you can go back to your original grid.) If you end up
with a contradiction, you know Alfred isn't Mr. Greene after all. And if you
end up with a complete answer with no contradictions, you've just solved the
puzzle! Sometimes the only way to solve a tough five-star puzzle is by
making and disproving assumptions.
But experienced solvers know that the most effective way to get unstuck is to put the puzzle aside for a while. Go on to other puzzles, and come back to the sticky one an hour, a day, or a week later. When you try the puzzle again with a clear mind, you'll probably see things you didn't notice the first time.
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