So a Hamiltonian path on an even-sided grid that starts on black will have to end on white.

因此，从黑色开始的偶边网格上的哈密顿路径必须以白色结束。

The challenge of the path problem is to find whether a given graph has a Hamiltonian path.

路径问题的挑战是找出给定的图是否具有哈密顿路径。

This puzzle is related to the Hamiltonian path problem named after the 19th century Irish mathematician William Rowan Hamilton.

这个谜题与以 19 世纪爱尔兰数学家 William Rowan Hamilton 命名的哈密顿路径问题有关。

In any grid with that configuration, a Hamiltonian path that starts and ends in opposite corners is impossible.

在具有该配置的任何网格中，一条在对角开始和结束的哈密顿路径是不可能的。

This puzzle adds a twist to the Hamiltonian path problem in that you have to start and end at specific points.

这个难题为哈密顿路径问题增加了一个转折点，因为您必须在特定点开始和结束。

But before you waste a ton of graph paper, you should know that a true Hamiltonian path isn't possible with these end points.

但是在你浪费大量方格纸之前，你应该知道真正的哈密顿路径对于这些端点是不可能的。

However, in any grid with even numbered sides, opposite corners are the same color, so it's impossible to start and end a Hamiltonian path on opposite corners.

然而， 在任何具有偶数边的网格中，对角是相同的颜色，因此不可能在对角上开始和结束哈密顿路径。