字幕列表 影片播放
-
You're the realm's greatest mathematician,
-
but ever since you criticized the Emperor's tax laws,
-
you've been locked in the dungeon
-
with only a marker to count the days.
-
But one day, you're suddenly brought before the Emperor
-
who looks even angrier than usual.
-
One of his twelve governors has been convicted of paying his taxes
-
with a counterfeit coin
-
which has already made its way into the treasury.
-
As the kingdom's greatest mathematician,
-
you've been granted a chance to earn your freedom by identifying the fake.
-
Before you are the twelve identical looking coins and a balance scale.
-
You know that the false coin will be very slightly lighter or heavier
-
than the rest.
-
But the Emperor's not a patient man.
-
You may only use the scale three times
-
before you'll be thrown back into the dungeon.
-
You look around for anything else you can use,
-
but there's nothing in the room -
-
just the coins,
-
the scale,
-
and your trusty marker.
-
How do you identify the counterfeit?
-
Pause here if you want to figure it out for yourself!
-
Answer in: 3
-
Answer in: 2
-
Answer in: 1
-
Obviously you can't weigh each coin against all of the others,
-
so you'll have to weigh several coins at the same time
-
by splitting the stack into multiple piles
-
then narrowing down where the false coin is.
-
Start by dividing the twelve coins into three equal piles of four.
-
Placing two of these on the scale gives us two possible outcomes.
-
If the two sides balance, all eight coins on the scale are real,
-
and the fake must be among the remaining four.
-
So how do you keep track of these results?
-
That's where the marker comes in.
-
Mark the eight authentic coins with a zero.
-
Now, take three of them and weigh them against three unmarked coins.
-
If they balance, the remaining unmarked coin must be the fake.
-
If they don't, draw a plus on the three unmarked coins if they're heavier
-
or a minus if they're lighter.
-
Now, take two of the newly marked coins and weigh them against each other.
-
If they balance, the third coin is fake.
-
Otherwise, look at their marks.
-
If they are plus coins, the heavier one is the imposter.
-
If they are marked with minus, it's the lighter one.
-
But what if the first two piles you weigh don't balance?
-
Mark the coins on the heavier side with a plus
-
and those on the lighter side with a minus.
-
You can also mark the remaining four coins with zeros
-
since you know the fake one is already somewhere on the scale.
-
Now, you'll need to think strategically
-
so you can remove all remaining ambiguity in just two more weighings.
-
To do this, you'll need to reassemble the piles.
-
One method is to replace three of the plus coins
-
with three of the minus coins,
-
and replace those with three of the zero coins.
-
>From here, you have three possibilities.
-
If the previously heavier side of the scale is still heavier,
-
that means either the remaining plus coin on that side
-
is actually the heavier one,
-
or the remaining minus coin on the lighter side
-
is actually the lighter one.
-
Choose either one of them, and weigh it against one of the regular coins
-
to see which is true.
-
If the previously heavier side became lighter,
-
that means one of the three minus coins you moved
-
is actually the lighter one.
-
Weigh two of them against each other.
-
If they balance, the third is counterfeit.
-
If not, the lighter one is.
-
Similarly, if the two sides balanced after your substitution,
-
then one of the three plus coins you removed
-
must be the heavier one.
-
Weigh two of them against each other.
-
If they balance, the third one is fake.
-
If not, then it's the heavier one.
-
The Emperor nods approvingly at your finding,
-
and the counterfeiting Lord takes your place in the dungeon.
