# Houston, We Have a Problem

Logic Level 2

A ​countdown number​ is a positive integer where the sum of each pair of consecutive digits forms part of a countdown. For example: 23120 is a countdown number because

\begin{aligned} &\boxed{2, 3}, 1, 2, 0 \longrightarrow 2 + 3 = \mathbf{5} \\ &2, \boxed{3, 1}, 2, 0 \longrightarrow 3 + 1 = \mathbf{4} \\ &2, 3, \boxed{1, 2}, 0 \longrightarrow 1 + 2 = \mathbf{3} \\ &2, 3, 1, \boxed{2, 0} \longrightarrow 2 + 3 = \mathbf{2} \\ \end{aligned}

What is the largest six-digit countdown number?

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