The Mathematical Ninja And The Cubes | Colin

The Mathematical Ninja glanced at the Rubik Cube and paused.

“And $45^3$ is…” A reach for the calculator. A flurry of colour. “Ow!”

“91,125,” said the Mathematical Ninja, catching the cube on the rebound and swizzling it solved. “Only needed 12 that time.”

The student sighed. “Go on, then. I bet there’s a trick.”

“Of course there’s a trick to cube a number ending in five. Let’s call it $(10n + 5)$.”

“Yes,” said the student, rubbing his hand. “Let’s.”

“Work out $\frac{n(n+1)(2n+1)}{2}$ — that’s to say, multiply the number of tens either side of your number and their sum.”

“Hold…

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