Note: When I refer to a bridge, I mean it in the non-mathematical sense
You are on a network of islands which are connected by wooden bridges and you want to see if you can burn every bridge in the island network. However, you can only burn a bridge once you've walked over it.
Once a bridge has been burned, it has gone and you cannot go back over it. None of the islands are connected.
Since you are going on a stroll, you cannot swim.
Given a list of the bridges and which islands they connect, output a truthy value if you can burn every bridge and falsey value if you cannot.
The input will be a list of numbers. A bridge is defined as:
Where are X and Y are integers. Each bridge has an integer number which X and Y refer to.
Means that there is a bridge between the islands 2 and 6.
The input will be a list of these bridges:
2,6 8,1 8,2 6,1
You may take this a flat array, if you wish.
The numbers for the islands will always be positive integers,
0 < n < 10. The island numbers will not always be contiguous.
When you walk over a bridge, you must burn it.
You will be given a maximum of eight islands. There is no limit on the number of bridges.
Island networks will always connect together. There will always be exactly one connected component.
This is an undirected network. For example, you can go either way across the bridge
Input > Output 1,2 1,3 1,3 1,4 1,4 2,3 2,4 > Falsey 1,5 1,6 2,3 2,6 3,5 5,6 > Truthy 1,2 1,3 1,4 2,3 2,4 3,4 > Falsey 1,2 > Truthy
Shortest code in bytes wins.