Problems
The problem of finding the longest path or cycle that is an induced subgraph of a given hypercube graph is known as the snake-in-the-box problem.
Szymanski's conjecture concerns the suitability of a hypercube as an network topology for communications. It states that, no matter how one chooses a permutation connecting each hypercube vertex to another vertex with which it should be connected, there is always a way to connect these pairs of vertices by paths that do not share any directed edge.
Read more about this topic: Hypercube Graph
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“The proper method of philosophy consists in clearly conceiving the insoluble problems in all their insolubility and then in simply contemplating them, fixedly and tirelessly, year after year, without any hope, patiently waiting.”
—Simone Weil (1909–1943)
“If we fail to meet our problems here, no one else in the world will do so. If we fail, the heart goes out of progressives throughout the world.”
—Eleanor Roosevelt (1884–1962)
“Those great ideas which come to you in your sleep just before you awake in morning, those solutions to the world’s problems which, in the light of day, turn out to be duds of the puniest order, couldn’t they be put to some use, after all?”
—Robert Benchley (1889–1945)