Logic Problem
I’ve been busy studying Logic and so here, instead of a newsworthy post, is a brain teaser courtesy of ITB106. If you like puzzles, you’ll love this. It’s hard:
You have 12 coins, and one of them is fake and so a slightly different weight. You also have a set of balances which only tell you if two things (or groups of things) are lighter or heavier than each other, or the same weight. Using the scales only three times, determine which is the fake coin. Note: you do not know whether the fake coin is lighter or heavier than the genuine coins, only that it is of a different weight.
Although infuriatingly tricky, it is possible to solve the puzzle. Let me know if you get it (and don’t cheat).
posted by monty · at 2:53 pm · filed under ETC
I. Weigh four coins on each side of the balance scale
a. If the balance is level, weigh two of the coins that balanced
(therefore, that are known to be real) and balance them against two of
the coins that weren’t balanced the first time
1. If the balance is level, take one of the coins you haven’t
tested yet and weigh it against one you know is coorect
Final: If the balance is level, the one coin you haven’t
checked is the fake
Final: If the balance isn’t level, the unknown coin on the
balance is the fake
2. If the balance isn’t level, weigh one of the two coins you
don’t know against one that you do
Final: If the balance is level, the coin that made the
balance unevel before is fake
Final: If the balance isn’t level, the unknown coin on the
balance is the fake
b. If the balance isn’t level, you know one of the eight is the
counterfiet. From now on, I will refer to the four that moved up as
“uppies” and the four that moved down as “downies”. Place two uppies
and a downie on each side of the balance
1. If the balance is level, take the two downies left out and
weigh one against a coin you know is real
Final: If the scale is level, the other downie is the fake
Final: If the scale isn’t level, the downie on the scale
(not the one you know) is fake
2. If the balance isn’t level, take the two uppies on the up
side and the downie on the down side. These are the only coins that
could’ve caused the scale to not be level since the downie could only
move the scale down and the uppies could only move it up. Place the two
uppies on opposite sides of the balance
Final: If the scale is level, the downie you took out is
fake
Final: If the scale isn’t level, whichever uppie is on the
higher side is fake (we know this since for it to be an uppie, it’d have
to be lighter)