Uploaded by TyYann on 03.10.2009

Transcript:

Hello and welcome to Seoul for the solution to my problem about

the smallest number that you can reverse

(revert?)

by multiplying by 9

So, here is...

...here is...

Here is how it works

(pardon my French...)

So, the important thing in this is to realize that

if a number works

then you're going to have the same number of digits from the beginning to the end

The number that you're going to

multiply by 9

is going to have the same number

of digits

than

the product of itself by 9.

so that's going to help us because

from this

we can start to analyze the problem.

Obviously,

I'm not going to show it here

one-digit numbers

are not going to work.

So let's try with two-digit numbers.

so we have

10 × 9 = 90

not so good but

we see here

that we're already very close to 100 which is a three-digit number.

And even closer, 11.

So if we get

to 12

which makes actually

108,

We know

that any big number like 12 or bigger are not going to work because

it's at least

three-digit numbers.

That's the first point

But this is going to give us a very important clue:

That if this, 12 × 9,

is a three-digit number,

so we know that

this, 120 × 9

is going to be a

four-digit number.

and it won't work either

and this, 1200 × 9

will be also

a five-digit number.

So, what we

get from this,

the a very important point, is

that the number we're looking for

actually starts by

1, 0

or by

1, 1,

we don't know the number of digits it has, it can be

three, four, five, we don't know,

but we know it starts with those two digits

so let's try

three digits.

Three digits makes what?

If we have a three-digit number starting by 1, 0,

and something

multiplied by 9

it's going to make something like 9;

maybe 0, maybe 1, we don't know exactly maybe anything

like this, but

we know that

this number is the reverse of that number

so it means that we have

obviously a 9 here.

And here

we should have that.

Unfortunately

when you multiply 109 by 9,

it doesn't it make

901.

So, this is not

the solution we're looking for

Let's try with 11.

11,

1, 1,

and something by 9,

and for the same consideration

1, 1, something multiplied by 9 makes

9, maybe something else, we don't know what digit is that

and then 2 and for the same considerations it's the reverse

so this should be 1, 1, 9

but 119 × 9

doesn't make...

it doesn't work actually,

it makes

1 here which is good

but here it makes 1 × 9 = 9 plus the 8

we had here

it makes actually

a four-digit number

So, this doesn't work either. So we need to find a

four-digit number that's going to start

either by 10

either by 11

and two digits

so let's start it.

We multiply by 9,

makes what?

obviously

this will be 0, 1 because it's reversed

and when you multiply 1 by 9 it has to make 9.

It could be bigger but if it's bigger

it's a five-digit number so it has to be 9

so it has to be 9 here

we make the same here and we get

1, 1, here

and of course

a 9 here.

so it makes a 9 here.

So what do we get now?

We have four-digit numbers with a hole.

We can try them all

but we can also try to find them easily because

These two numbers have to be

multiples of 9

and we know or we should know that any multiple of 9, if you add

their digits

and you get also a multiple of 9

So 9 + 1 + 1

makes

9 + 1 + 1

makes 11

and 11

if you want to

make it a multiple of 9, you have to add up 7

and unfortunately

This is not

This is not going to work. If you multiply,

you get a different result, this is not true.

If we try the same reasoning here,

we know that to have a multiple of 9 here we have to have an 8.

And 8 of course here.

And you know what?

One thousand

and eighty-nine

is the solution we are looking for.

Since we started with the smallest number and continued by getting

bigger and bigger

and finally we got this one,

this is the smallest one different from 0

that works

and this is the solution

to the problem I gave you.

I hope I didn't explain it too fast I think

you can pause the video and

see it again

and this is the solution of this

Well, you can try with a calculator anyways and see that

it actually works.

See you next time for another video and for another problem,

I hope as usual

that you enjoyed this one, Bye bye!

the smallest number that you can reverse

(revert?)

by multiplying by 9

So, here is...

...here is...

Here is how it works

(pardon my French...)

So, the important thing in this is to realize that

if a number works

then you're going to have the same number of digits from the beginning to the end

The number that you're going to

multiply by 9

is going to have the same number

of digits

than

the product of itself by 9.

so that's going to help us because

from this

we can start to analyze the problem.

Obviously,

I'm not going to show it here

one-digit numbers

are not going to work.

So let's try with two-digit numbers.

so we have

10 × 9 = 90

not so good but

we see here

that we're already very close to 100 which is a three-digit number.

And even closer, 11.

So if we get

to 12

which makes actually

108,

We know

that any big number like 12 or bigger are not going to work because

it's at least

three-digit numbers.

That's the first point

But this is going to give us a very important clue:

That if this, 12 × 9,

is a three-digit number,

so we know that

this, 120 × 9

is going to be a

four-digit number.

and it won't work either

and this, 1200 × 9

will be also

a five-digit number.

So, what we

get from this,

the a very important point, is

that the number we're looking for

actually starts by

1, 0

or by

1, 1,

we don't know the number of digits it has, it can be

three, four, five, we don't know,

but we know it starts with those two digits

so let's try

three digits.

Three digits makes what?

If we have a three-digit number starting by 1, 0,

and something

multiplied by 9

it's going to make something like 9;

maybe 0, maybe 1, we don't know exactly maybe anything

like this, but

we know that

this number is the reverse of that number

so it means that we have

obviously a 9 here.

And here

we should have that.

Unfortunately

when you multiply 109 by 9,

it doesn't it make

901.

So, this is not

the solution we're looking for

Let's try with 11.

11,

1, 1,

and something by 9,

and for the same consideration

1, 1, something multiplied by 9 makes

9, maybe something else, we don't know what digit is that

and then 2 and for the same considerations it's the reverse

so this should be 1, 1, 9

but 119 × 9

doesn't make...

it doesn't work actually,

it makes

1 here which is good

but here it makes 1 × 9 = 9 plus the 8

we had here

it makes actually

a four-digit number

So, this doesn't work either. So we need to find a

four-digit number that's going to start

either by 10

either by 11

and two digits

so let's start it.

We multiply by 9,

makes what?

obviously

this will be 0, 1 because it's reversed

and when you multiply 1 by 9 it has to make 9.

It could be bigger but if it's bigger

it's a five-digit number so it has to be 9

so it has to be 9 here

we make the same here and we get

1, 1, here

and of course

a 9 here.

so it makes a 9 here.

So what do we get now?

We have four-digit numbers with a hole.

We can try them all

but we can also try to find them easily because

These two numbers have to be

multiples of 9

and we know or we should know that any multiple of 9, if you add

their digits

and you get also a multiple of 9

So 9 + 1 + 1

makes

9 + 1 + 1

makes 11

and 11

if you want to

make it a multiple of 9, you have to add up 7

and unfortunately

This is not

This is not going to work. If you multiply,

you get a different result, this is not true.

If we try the same reasoning here,

we know that to have a multiple of 9 here we have to have an 8.

And 8 of course here.

And you know what?

One thousand

and eighty-nine

is the solution we are looking for.

Since we started with the smallest number and continued by getting

bigger and bigger

and finally we got this one,

this is the smallest one different from 0

that works

and this is the solution

to the problem I gave you.

I hope I didn't explain it too fast I think

you can pause the video and

see it again

and this is the solution of this

Well, you can try with a calculator anyways and see that

it actually works.

See you next time for another video and for another problem,

I hope as usual

that you enjoyed this one, Bye bye!