15 Puzzle

Algebra Level 4

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

⌊ det ⁡ ( e A ) ⌋ . \lfloor \det (e^A) \rfloor.


The answer is 65659969.

Steven Zheng by Steven Zheng , 26, China

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1 solution

Joseph Miller
Aug 7, 2014

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

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice job. I have a note for that fact. Check out

Unique Matrix Function

Steven Zheng - 6 years, 10 months ago

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