2178 times 4 makes 8712 math problem solution

Uploaded by TyYann on 03.10.2009

Hello and welcome to Seoul for the solution to my problem about
the smallest number that you can reverse
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
the product of itself by 9.
so that's going to help us because
from this
we can start to analyze the problem.
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
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.
when you multiply 109 by 9,
it doesn't it make
So, this is not
the solution we're looking for
Let's try with 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?
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
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!