*These are two puzzles I arrived at while working on my
PhD thesis. I know the answers but not because I derived them. I
think both puzzles are quite hard. Have fun!*

**Typesetting.** As you know from a previous post,
ViM
doesn’t handle paragraph reformatting very well in L^{A}T_{E}X, so I
wrote a small tool. Given word lengths *l*_{1}, *l*_{2}, …, *l*_{n}
we want to insert line breaks such that (1) no line is longer
than *l* and (2) the shortest line is as long as possible. Here’s
the challenge: do it in *O*(*n*) time.

**Inequality.** Show that the following inequality has no
solution in non-negative reals (or integers if you prefer).

PS: I know the answers because of 11011110 and, respectively, geomblog.

## 3 comments:

Just to make it explicit: The statement of problem

Inequalityis obfuscated to make it harder. I'll `deobfuscate' it when I post the answer. (The question is the same as something I asked on Mathoverflow, so you can view the answer there if you are impatient.)Hi,

I'm writing (mostly written) a project for automatic programming exercise grading! (reith.bshellz.net/projects/tsi/) where i find your project on Ohloh, surprised! but can't find your E-mail address. maybe can we have share or experiences.

Sorry for irrelevant comment

The inequality should say `greater or equal': Equality is obtained, for example, for b=f=1, and all others set to zero.

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