I don't even have this cube!

Computer Science Level pending

This is a \( \displaystyle 4\times 4\times 4 \) Rubik's cube. It has \( \displaystyle 401 196 841 564 901 869 874 093 974 498 574 336 000 000 000 \) combinations! It has 9 trailing zeroes.

Find the number of trailing zeroes in the number of combinations of the \( \displaystyle 25\times25\times25 \) Rubik's cube.

Details:

  • Do not disassemble the cube, it's expensive.
  • Calculators are allowed.
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