Uploaded by TyYann on 29.09.2009

Transcript:

Hello and welcome to Seoul for the solution for my chain number problem

or number chain problem... Whatever!

So, in the previous video

the problem video

there was

it was a big hint

The hint was: the solution is unique

I asked you to find the right one

the one

that has

the longest chain.

and this is what we're going to use to find THE solution

So, if you remember

I gave you as an example 25

Imagine that 25

is THE solution.

25 makes

if you remember

a chain of 3

2 × 5 = 10; 1 × 0 = 0 That makes a 3-step chain.

So, imagine this is the solution

if this is the solution,

there is a another solutions, 52 because 25 and 52,

if you multiply them

you get the same result

and I told you the answer is unique.

So obviously

25

25 or 52,

are not the solution

so which numbers among here

which numbers among

between 1 and 99

Well, you have all those

one-digit because when

you reverse them it's still the same number so if one of them is the solution, it's unique.

obviously it's not the solution because we know what it is a 1-step chain

because we don't multiply and we don't do anything with those so,

those are not the solution

but there are others like 10

because the equivalent of 10, 01, doesn't exist.

the one that exists is 1 and it's a stop

So this one has no equivalent when you reverse it.

so if this one is the solution it's unique.

unfortunately all those numbers that end by 0

make a very very short chain because 0 × 1 = 0 and

over, it's always a 2-step chain

and we know

because we tried already with 25 that 25 is already longer

it's a three-step chain

so

so so so

which numbers can work?

There are few of them remaining actually

They are 11

22

33

44

55

66

77

88

and 99. Those can work

Only those

Because when you reverse them of course i'ts the same numbers so if

one of them is the solution

then it's unique

and that's exactly what we're looking for

So, we just have to compute those

1 × 1 = 1,

it's over

4, it's over

9 it's over

this is a little bit more interesting

but still it's a 3-step chain

and it's over.

This one

it's a 4-step

we recognize our 25

which is our

3-step chain

And this is the 55. 4 steps... Getting good, but

this is also

like this

like this

and there's another 4-step so

since the solution is unique there's great chances that those are not

the solution and the solution is bigger. Bigger? Let's try bigger actually

Well, bigger is a little bit

not so good

bigger is not better, not always better.

This one, maybe?

4-step chain, another one.

One, two, three 4-step chains, for a unique solution it's a little bit of a problem

But if we try this one,

of course I kept it for the end,

everybody understands why,

it makes 49

36

18

and finally... 8

And you get a 1, 2, 3, 4,

and 5-step chain

which is the longest

among the numbers from 1 to

99

so 77

is the answer

because the answer

we said it, is unique

so we could find it

easily.

I hope you enjoyed this problem

and see you next time for the next one.

Bye, bye!

or number chain problem... Whatever!

So, in the previous video

the problem video

there was

it was a big hint

The hint was: the solution is unique

I asked you to find the right one

the one

that has

the longest chain.

and this is what we're going to use to find THE solution

So, if you remember

I gave you as an example 25

Imagine that 25

is THE solution.

25 makes

if you remember

a chain of 3

2 × 5 = 10; 1 × 0 = 0 That makes a 3-step chain.

So, imagine this is the solution

if this is the solution,

there is a another solutions, 52 because 25 and 52,

if you multiply them

you get the same result

and I told you the answer is unique.

So obviously

25

25 or 52,

are not the solution

so which numbers among here

which numbers among

between 1 and 99

Well, you have all those

one-digit because when

you reverse them it's still the same number so if one of them is the solution, it's unique.

obviously it's not the solution because we know what it is a 1-step chain

because we don't multiply and we don't do anything with those so,

those are not the solution

but there are others like 10

because the equivalent of 10, 01, doesn't exist.

the one that exists is 1 and it's a stop

So this one has no equivalent when you reverse it.

so if this one is the solution it's unique.

unfortunately all those numbers that end by 0

make a very very short chain because 0 × 1 = 0 and

over, it's always a 2-step chain

and we know

because we tried already with 25 that 25 is already longer

it's a three-step chain

so

so so so

which numbers can work?

There are few of them remaining actually

They are 11

22

33

44

55

66

77

88

and 99. Those can work

Only those

Because when you reverse them of course i'ts the same numbers so if

one of them is the solution

then it's unique

and that's exactly what we're looking for

So, we just have to compute those

1 × 1 = 1,

it's over

4, it's over

9 it's over

this is a little bit more interesting

but still it's a 3-step chain

and it's over.

This one

it's a 4-step

we recognize our 25

which is our

3-step chain

And this is the 55. 4 steps... Getting good, but

this is also

like this

like this

and there's another 4-step so

since the solution is unique there's great chances that those are not

the solution and the solution is bigger. Bigger? Let's try bigger actually

Well, bigger is a little bit

not so good

bigger is not better, not always better.

This one, maybe?

4-step chain, another one.

One, two, three 4-step chains, for a unique solution it's a little bit of a problem

But if we try this one,

of course I kept it for the end,

everybody understands why,

it makes 49

36

18

and finally... 8

And you get a 1, 2, 3, 4,

and 5-step chain

which is the longest

among the numbers from 1 to

99

so 77

is the answer

because the answer

we said it, is unique

so we could find it

easily.

I hope you enjoyed this problem

and see you next time for the next one.

Bye, bye!