An Arithmatical Trick

“I'll give you an arithmatical trick and ask you to explain it. One of you – you, Professor, if you like – write down a three-digit number, but don't tell me what it is.”

“Can we have any noughts in it?”

“I set no reservations. You can wirte down any three numerals you want.”

“All right, I've done it. What next?”

“Write the same number alongside. Now you have a six-digit number.”

“Right.”

“Pass the slip to your neighbor, the one farther away from me, and let him divide this six-digit number by seven.”

“It's easy for you to say that, and what if it can't be done?”

“Don't worry, it can.”

“How can you be so sure when you haven't seen the number?”

“We'll talk after you've divided it.”

“You're right. It does divide.”

“Now pass the result to your neighbor, but don't tell me what it is. Let him divide it by 11.”

“Think you'll have your own way again?”

“Go ahead, divide it. There'll be no remainder.”

“You're right again. Now what?”

“Pass the result on and let the next man divide it, say, by 13.”

“That's a bad choice. There are very few numbers that are divisible by 13... You're certainly lucky, this one is!”

“Now give me the slip, but fold it so that I don't see the number.”

Without unfolding the slip, the man passed it on to the professor.
“Here is your number. Correct?”

“Absolutely.” The professor was surprised. “That is the number I wrote down.”