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Resolución de problemas, resolviendo un problema más simple.
What was that again?
How long would it take us to get from Earth to Mars if we traveled at the speed of light?
What was that?
I think it was 300,000 kilometers per second.
Or was it millions?
My head hurts.
Oh, my stomach.
We both need a good meal.
Yes.
Have you ever had a problem like this, so terrible that your head hurts just thinking about it?
Only 20 times a day.
Or when the numbers are so big that you can't hold them in your head?
Or when I think about the money I owe for my bike.
Well, a way to handle big numbers is by simplifying them.
That's right. By simplifying the numbers we can see more clearly what the problem is.
And that's what should be done with computers so that the numbers involved are not so terrible.
I wonder if they would have had the same problem as in place of Earth and Mars.
What would have been the distance between their houses?
Well, if Sam lives three kilometers from the warehouse and Cree lives six kilometers from the warehouse,
how long would it take Mike to go by bike between their houses if they were three kilometers per hour?
Can you calculate it?
Of course.
Like the three kilometers of the warehouse, it's six kilometers.
That leaves me with three kilometers between the two houses,
which obviously means that there is only one hour of travel.
But those are simple numbers.
That's the idea.
It's the same problem they had with the boys, but explained with simple numbers.
Look, where do we start?
Well, the distance between the Sun and the Earth is 150 million kilometers.
Yes, the distance between the Sun and Mars is 228 million kilometers.
Wow.
Don't say wow.
Why not?
So that the numbers seem very large.
But they are large.
Okay.
But if we could assume that they weren't walking, it would be easier.
That's right.
What is it?
Here, Carlos.
How?
Well, let's think about the distance between the Sun and the Earth,
but not like 150 million kilometers, just like 150.
Then we can calculate what we do with them.
Okay.
Well, let's turn 228 million kilometers into 228 kilometers.
Then what?
Let's add 150 plus 228.
No, you don't have to add.
You have to subtract.
Look, do you see the parts?
Let's say this is the Sun.
This is the Earth.
And can I take this?
This is Mars.
Okay.
There are 150 kilometers between this and this, and 228 between this and this.
So how much is there between these two?
We already know the total distance.
We are trying to calculate the distance between these two.
So we have to subtract 228 minus 150.
78 kilometers?
Yes, 78 kilometers.
Correct.
But the question was a million.
So the distance between Earth and Mars is 78 million kilometers.
Wow!
Driving big numbers can be tremendous.
Until you learn to calculate them.
A man who drives big numbers is Ivan Sonyak,
a gastronomic researcher from Lontarios in Centros.
There are billions and billions of galaxies.
Each one contains billions of stars,
and the distance between these stars would often take a human life to get from one point to another.
As an astronomer, I drive big numbers every day.
Astronomy is full of big numbers simply because the space is so vast.
Imagine that we could bring the Sun, the Earth and all the planets in our room.
The average distance between the Sun and the Earth is 150 billion kilometers.
But if we could reduce it by 15 centimeters, that is only the size of a palm.
Here is the Sun, here is the Moon, only 15 centimeters away.
Now this is my question.
If we bring the rest of the solar system here so that it matches the size and we choose the furthest planet, the planet Pluto,
and this is what I want to ask you, how far do you think Pluto should be to fit into this system?
You may think that it could be, let's say, one meter further, or two meters, or even a little further than that.
But it turns out that even on this scale, to put Pluto on the right place,
it should not only be at the end of the room, but behind the door, down in a hall.
I should have a very good arm to throw this thing as far as Pluto really is,
even if we only place the Sun and the Earth 15 centimeters away.
The space is huge, but what we can do is play with the distances.
We can narrow them down in our imagination.
Why bowling? Why can't it be basketball or something else that I play well? I hate bowling.
That's what the vote was for.
So let's finish with this subject.
Supposedly, each child in the class will bowl against each of the rest of the children.
How many games will be played?
I'm sure 20 games.
How did you calculate it?
There are 20 children in the class.
Yes?
Probably 20.
Wait. There are 20 children in the class, so each one will bowl against the other.
So it's 19 games each.
That's right. 19 games per piece.
There are 20 children in the class, so each one will bowl 20 times 19.
That's 380 games.
That's wrong.
Yes.
If we three played against each other, I would play against Sam and against Mike.
Sam against Mike and against me.
But we've already counted the games.
So we'll play against each other.
I'll play against Sam and against Mike.
Sam against Mike and against me.
Sam against Mike and against me. But we've already counted that.
And Mike would play against me, which we've already counted.
And Sam, which we've already counted.
Then we'll only play three games.
And that's not helping us with the other 20 children in the class.
We'll try with four.
Let's suppose that Billy also wants to come here.
So I'd play against Sam, Mike and Bill.
That's three.
And Sam against Mike and Bill.
Not against me because I've already counted.
So that's two.
And then Mike would play against Bill.
But not against Sam or me because we've already counted those games.
That's one.
We're not counting Billy because he's already counted all his games.
So we're only counting the number of games.
Three plus two plus one plus zero. Six games.
I think we found something here.
So for three players it would be two plus one plus zero.
And for four players it would be three plus two plus one plus zero.
Yes, if we have five players it would be four plus three plus two plus one plus zero.
That's a system, boss.
With 20 like us it's 19 plus 18.
So far we've seen a couple of strategies to solve a problem in an easier way.
One is to check large numbers and thus make them more manageable.
And the second is to form a model 5 and then apply it to a more complicated problem.
Another strategy is to divide a problem into steps.
Look at this.
I can't believe it.
Believe it.
What a basketball.
Hey, look here.
What does it say?
A key for you.
I live on Avenue Lee.
You figure out the number.
I'll meet you later.
Attention, sir.
Good guy.
Attention.
I would say we should catch that guy.
What is that?
How do you break heads with numbers?
Let's see. Where do we start?
Let's see.
20.
Okay.
20 minus 3 is 17.
For 4 is 78.
For 5 is 73.
Divide 9.
That's wrong.
Let's try with 7.
7 minus 3 is 4.
For 4 is 16.
For 5 is 21.
Divide 9 is 2.
With something.
Oh, that's wrong.
Let's try with 17.
No, that's wrong.
We can't try anything.
We'll be like this forever.
Well, what do you think?
I don't know.
Let's do this step by step.
What do we know?
That the final number is 5.
You're right, it's 5.
So we have to work backwards to move forward.
What's divide 9?
9 is 5.
What's divide 9?
9 is 5.
45.
So the second step is what?
What number plus 5 is 45.
40.
What number multiplied by 4 is 40.
45.
What number minus 3 is 10?
13.
That's that stupid Bernie Pepper.
He lives in Lee 13.
So we'll find him there on Friday.
Very good.
Hey, wait.
What time?
It's 5.
Okay, so what do we know?
That the final number is 18.
So what we have to calculate is what number multiplied by 6 is 18?
3.
Okay, second step.
What's divide 9?
9 is 3.
27.
And what do we do?
Plus 12 is 27.
15.
Hey, hey, we're doing it right.
15, 15.
9 is 3.
And something minus 2 is 3?
5.
1 and 3, 5.
Wait a minute.
Maybe we should do something special for him.
To thank him.
Something special, a good idea.
Special, yes.
And you know what?
What?
Who?
Yes, it's me.
Really?
Yes.
Solvate was supported in part by the National Science Foundation.
This program was produced for AIT by the FilmWorks.
This program is produced under the supervision of the National Science Foundation.