whoosh

“Long time, no see, sensei.”

Short time, always see. The Mathematical Ninja pointed at their eyes with two fingers, back to me, and back to their eyes.

“I suppose you’re here about the ‘I suppose it’s about 50’ I recently muttered. I did feel a sudden chill pass through the room.”

Indeed.

“I can’t even remember the sum. Was it $100 \div 1.9$?” I ducked to dodge the dagger flung my way; the Ninja’s response to a $\div$ is tiresomely predictable.

It was. And the result is $52.\dot 63157894736842105\dot2$. How they pronounced the dots, I can’t tell you. They transmit the LaTeX directly into my brain.

“I stand by ‘about 50, possibly a little more’ for a question about apples.”

I might have let ‘52’ go unchallenged.

“I expect you have a recipe for the recurring bit.”

You expect correctly. The rule for a given digit is to add ten if the previous digit was odd, then halve to get the next digit. Ignore remainders.

“So starting from that 6 straight after the dot…” (another dagger, another dodge) “… its previous digit is 2, so we don’t add 10; halve it to get 3.”

Correct.

“Then three’s previous digit is 6, we don’t add 10, we just halve and ignore the remainder to get 1.”

Yes.

“But the 1’s previous digit was odd, so we need to halve 11 to get 5, ignoring the remainder.”

Are you going to keep doing this until it start to recur? I believe the instructions were perfectly clear, and I trust that you wouldn’t doubt me.

“Of course not, sensei,” I said, surreptitiously closing down Wolfram Alpha. “Wouldn’t dream of it.”