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A
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be a square matrix represented by above the 15 puzzle. The empty slot is 0. Find

$\lfloor \det (e^A) \rfloor.$

The answer is 65659969.

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From the fact that $\left| { e }^{ A } \right| ={ e }^{ Tr(A) }$ we get $\lfloor \left| e^A \right| \rfloor = \lfloor e^{1+6+11+0} \rfloor$ which by calculator computation is $\boxed { 65659969. }$