employer of last resort

I’ve been reading about these “job guarantee” or “employer of last resort” theories, and they seem interesting. Basically the government provides employment at delta below the legal minimum wage for those who are unemployed, thereby absorbing excess labor into the public sector. The advantages are clear: it is certainly better than welfare and it doesn’t compete with the private sector.

Why is this? Let’s reason about it in a crude way.
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triangular pursuit

Here’s a problem posed to me by a friend:

Consider an equilateral triangle ABC with edge length 1. At each vertex is an object that is capable of movement at exactly speed 1. Beginning at time 0, each of the three objects moves toward its initial adjacent neighbor object, as in a game of pursuit. Of course, by symmetry, the objects will meet at the incenter of ABC. The question: how far will they have traveled?
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