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Let $S$ be a set of strings over $0,1$ such that if $x$ is in $S$

$x$ has $\le k-1\quad$ $0$'s

$x$ has $\le k-1\quad$ $1$'s

What is the MAX that $\sum_{x\in S} |x|$ can be?

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    (I admit, despite my answer below I'm a little confused by the question of 'MAX' here - there's nothing to indicate what variable the maximum is being taken over. My presumption is that it's the max over all sets $S$ satisfying the condition, but there's clearly an easily-defined set $S_0$ which contains _all_ $x$ satisfying the conditions specified, and the value of the max is then just the value of the sum over $x\in S_0$.)2011-07-08

2 Answers 2