##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Steve Butler

#### Department of Mathematics UCLA

## Orienting the Edges of the Hypercube With Only Two In-degrees

##### Abstract:

\indent We show that it is possible to orient the edges of the $n$-dimensional cube so that only the in-degrees $a$ and $b$ occur if and only if the two obvious necessary conditions hold, namely there are nonnegative integers $s$ and $t$ so that $s+t=2^n$ and $as+bt=n2^{n-1}$. This is connected to a question arising from constructing strategies for a type of hat game with $n$ players so that regardless of placements the number of correct guesses is $a$ or $b$. Joint work with Joe Buhler, Ron Graham and Eric Tressler

### November 2, 2010

### 4:00 PM

### AP&M 7321

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