## Problem of the Day #372: Binary Tree Path Lengths
*March 25, 2012*

*Posted by Alex in : potd , trackback*

*Inspired by a problem from the 2012 TJ IOI.*

The nodes in a complete binary tree of infinite height are referred to by ordered pairs $(x, y)$, where $x$ and $y$ are 0-indexed values denoting the row and the column of the nodes. The root is $(0, 0)$. Find the length of the shortest path between node $(1000, 3)$ and $(1234, 123456)$.

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