00:01
In this problem, our job is to determine whether the traveler can fly from city 1 to city 9.
00:07
We're told that there's a flight from one city to another if and only if we write those numbers down and form a two -digit number, and that number has to be divisible by 3.
00:18
So we're going to list the possible flights.
00:22
Then we will set up a graph to demonstrate the possible flights between cities.
00:28
So from city 1, a traveler can fly to city 2 because 12 is 10.
00:33
Divisible by three, or to city five, or to city 18.
00:40
From city two, a traveler can fly back to city one, or to city four, or to city 27.
00:50
From city three, the only possible flights are to city six and city nine.
00:56
We're not going to have flights from one city to itself.
01:00
So just two possible flights from city three, from city four, you can fly to city two, city five, or city 8.
01:11
From city 5, you can fly to 1 or 4 or 7.
01:18
From city 6, the situation is the same as with 3.
01:21
You can fly to 3 or to 9.
01:24
Those are the only choices.
01:27
So let's sort of keep me straight here.
01:30
There we go.
01:31
From city 7, you can fly to 2 or 5 or 8.
01:37
From city 8, you can fly to 1 or 4 or 7.
01:42
And finally, from city 8.
01:43
City 9, you can fly to 3 or 6.
01:47
So here are the possible flights where we have counted a flight from 1 to 2 separately from 2 to 1.
01:53
So we see from this list that there are 24 possible flights at all.
02:01
So let's set up a graph...