A Maths Puzzle: LogicYouTube↗  IA↗(long shot)
Education  101.8K views 711 likes 33 dislikes   15 May 2008
singingbanana 228K subscribers United Kingdom YouTube↗


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Contributed subtitles
Dutch Angela Flierman
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Hello, everybody.
everybody well first of all welcome to
Well, first of all--welcome to my office.
my office
As you can clearly see,
as you can clearly see it really is a
it really is a magical place.
magical place today I have a logic
Today, I have a logic puzzle for you. I have four cards.
puzzle for you I have four cards one on
And on each card,
each card is a letter on one side and
is a letter on one side, and a number on the other side.
another boat on the other side now I
Now, I've shuffled them,
have shuffled them and laid them out and
I've laid them out, and they read D-K-3-7.
they read DK three seven and I'm going
And I'm going to make a conjecture
to make a conjecture about these four
about these four cards, and the conjecture is this:
cards and conjectures this every card
Every card with a 'D' on one side
within D on one side has a three on the
has a '3' on the other.
other now I don't know whether this
Now, I don't know whether this statement is true or false.
statement is true or false so which
So which cards do I need to turn over
cards do I need to turn over to
to determine the validity of the statement?
determine the validity of the statement
I could turn over all four cards,
I could turn over all four cards and
and that would tell me whether it was true or not,
that would tell me whether it was true
but what is the minimum number of cards
or not but what is the minimum number of
I need to turn over
cards I need to turn over to determine
to determine whether the statement is true?
whether a statement is true well while
Well, while you're thinking about that,
you're thinking about that let me
let me describe another problem.
describe another problem for guys walk
Four guys walk into a bar.
into a bar one of the waters of whiskey
One of them orders a whiskey, one orders a Coke,
while orders a coke one is an older
one is an older gentleman,
gentleman and one isn't your guy in a
and one is a young guy in a hoodie. And, as you know, in a bar,
hoodie and as you know in a bar everyone
everyone that orders an alcoholic drink
that orders a now Holly drink must be of
must be of legal age. So who do we need to ID?
legal age so who do we need to ID well
Well,
it shouldn't be too hard to see we need
it shouldn't be too hard to see. We need to ID the whiskey drinker,
to only you the whiskey drinker and the
and the young guy in the hoodie.
ongoing hooding it's irrelevant to ID
It's irrelevant to ID the Coke drinker, and the idea is
the coke drinker and the idea is and the
the older guy is clearly over age,
older guy most clearly arranged so we
so we don't need to ID him.
don't need to ID him
Well, this principle
well this principle can be applied to
can be applied to the problem behind me.
the problem behind me which cars do we
Which cards do we need to turn over?
need to turn over well let's go through
Well, let's go through them one by one. What about D?
them one by one what about the way
Well, it shouldn't be too hard to see
shouldn't be too hard to see if D had
that if D had another number, other than 3,
another other than three on the other
on the other side, the statement would be false,
side the statement false so we do need
so we do need to check D.
to check thee and in this case the
And, in this case, D has a 3 on the other side.
hazard leaned on his
So, so far, so good. Now, what about K?
so so far so good now what about 2k well
Well, just like in the other problem,
just like in the other problem K isn't
K is, in fact, irrelevant.
that irrelevant it doesn't matter what's
It doesn't matter what's on the other side.
on the other side we don't need to check
We don't need to check it. We can--it has a 1 on the other side--doesn't matter.
it become it has a 1 on the other side doesn't matter
Now, what about 3? Do we need to check card 3? Well, this statement is, in fact, an If and Then statement in disguise. So, If a card has a 'D' on one side,
now what about 3 do we need to check card 3 well this statement isn't that an if and then statement in disguise so if a card has indeed on one side then it
Then it has a '3' on the other.
has 3 on the other side the implication
The implication is in one direction.
is in one dimension so in fact it is
So, in fact, it is irrelevant
irrelevant what's on the other side of
what's on the other side of this card. It could be D, it could not be--it doesn't matter. In this case, it's P.
this card it could be d could not be doesn't matter in this case it's a P and
And what about card 7?
what else can't 7 do we need to check
Do we need to check card 7? Well, if you think about it,
card center but if you think about it if
if 7 has a D on the other side,
7 that has a deal on the other side and
then the statement would be false,
this thing probably false so we do need
so we do need to check it, and, in this case, it does have a D,
to check it and in this case it does not
so the statement is false.
a decent thing to suppose I could have
I could have used this card
used this card which has an R on the
which has an R on the other side,
other side and the statement would have
and the statement would have been true.
been trimming the cards we need to check
But the cards we need to check, then are D and 7. How did you do?
then d and sin how did he do well in
Well, in many surveys, they have found that
many surveys they have found that about
about 10 percent of the general public
10% of the general public getting this
get this question correct.
question correct in fact the reason so
In fact, a recent survey found again that ten percent of the general public
that they found again that 10% of the
got this correct,
general public got this correct 29% of
twenty-nine percent of mathematics undergraduates
mathematics undergraduates got the
got the correct answer, and only forty-three percent of mathematicians themselves
correct answer and only 43% of mathematicians themselves got the
got the correct answer.
correct answer so how did you do
So how did you do? Are you smarter than fifty-seven percent of mathematicians?
are you smart enough 57% petitions let me know in the comments
Let me know in the comments below.
below
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