“Sensei! I have a problem!”

The Mathematical Ninja nodded. “Bring it on.”

“There’s a challenge! Someone has picked a five-digit integer and cubed it to get 6,996,364,932,376. I know it ends with a six, and I could probably get the penultimate digit with a bit of work… I just wondered if there was a better way. Without a calculator, of course.”

The Mathematical Ninja hmmed for a moment. “Tricky.”

The student’s eyes boggled. This was not a word he had heard escape the Mathematical Ninja’s lips before.

“It’s a tiny bit less than $7 \times 10^{12}$,” said the Mathematical Ninja,…

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