Let \(\ddot { x } ={ x }^{ x }\cdot { (x-1) }^{ x-1 }\cdot { (x-2) }^{ x-2 }\cdot { (x-3) }^{ x-3 }......\cdot 1\).

Example: \(\ddot { 5 } ={ 5 }^{ 5 }\cdot { 4 }^{ 4 }\cdot { 3 }^{ 3 }\cdot { 2 }^{ 2 }\cdot 1\)

Then \(\ddot { 10 }\) would end in how many terminating zeroes?

(Please post a solution.)

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