Warning: If you hate having a logic puzzle you can't solve,
you should stop reading now.
The problem with most logic puzzles is that they are inelegant.
They either rely on difficult mathematical concepts, long induction
chains, phrasings based on puns / cultural assumptions, or
totally anti-climatic "lateral thinking" surprises. And of the
few elegant logic puzzles left, many are too well-known (i.e., the
3 light-bulbs problem).
I think an elegant logic puzzle
is one that can be told to anyone age 10 and up and doesn't
rely on gimmicks, but always seems impossible to anyone
when first told. In other words, the problem is tough but the
solution is satisfactorily simple once explained. The solution
doesn't involve a person or tool that wasn't explicitly
stated in the problem itself.
What follows are two logic puzzles I've found that
I think are elegant but which are relatively unknown. To increase
the challenge, I will not post the solutions here (nor will I
tell you even if you email me). Furthermore, I have altered the
phrasings and context such that similar versions of the puzzles
can't be easily googled.
Galendor and Kellen are two spies working for the same underground organization.
Galendor has recently stolen a rare artifact - The Mithril
Amulet - from the Queen of Rengefall. Galendor must pass the
artifact to Kellen to be transported out of Rengefall but the
Queen's henchmen are closing in on them.
Galendor and Kellen are staying in two different rooms in a tavern at
the border of Rengefall. Because of the henchmen, neither of
them can leave the room tonight for fear of being caught. Thus,
the only way that Galendor and Kellen can transfer objects
between each other is via the tavern servants.
The problem is that all the servants in the tavern are known to be thieves
and will steal anything that is not secure. Both Galendor and
Kellen have an iron safe with a large clasp that can be secured
with a padlock. Both of them have a padlock and its corresponding
key. In other words, there is 1 Amulet, 2 Safes, 2 Padlocks,
and 2 correponding Keys.
Anything that is not padlocked in a safe will be stolen by the servants.
This includes any unlocked padlocks, keys, and of course the
Amulet itself. Given these constraints, how did Galendor manage
to transfer the Amulet to Kellen?
One Hundred Copper Coins
In Rengefall, copper coins are minted with the portrait of the Queen on
one side and the portrait of the King on the other side.
On this day, the half-crazed executioner gives the captured Talin one
chance to avoid execution. The executioner brings Talin into
an unlit room. He tells Talin that scattered on the table in
front of him are one hundred copper coins of which twenty have
the Queen side facing up while the rest have the King side
facing up. If Talin can separate the coins into two piles, each with
the same number of Queens facing up, he will release Talin.
One other constraint is that Talin must accomplish this task
in 5 minutes. If Talin fails, he will be beheaded.
It is impossible for Talin to see which side the coins are facing up in
the darkness, and the contours of the portraits are too similar
to decipher by touch. Nevertheless, Talin managed to separate
the coins into two piles with the same number of Queens facing
up in the time allotted. How did he accomplish this?
(The correct answer does not involve standing coins on their edges. Elegant
logic puzzles do not involve semantic loopholes.)