TL;DR see below mapping between numbers and other numbers. How does the mapping work?

Intel has come in about a secret organization that gathers once a week at a specific time and place to discuss it's strategy. I did not know what they were up to, but I was determined to find out. I've decided to infiltrate them with the help of my partner who stayed at home and discretely stayed on the phone with me, whispering hints in my ear piece.

We knew that to enter one must know some kind of password or code. The members of the society were often arrogant about the prospects of an outsider for breaking their code, especially someone like me, but I was determined.

The moment of truth has come. I've followed someone to the meeting place, and I'm about to try and get in.

Girl: "You can't come in here"

Me: "Why not? I'm a member"

Girl: (Whispering to another girl and giggling)

Me: "Are you gonna let me in?"

Girl: "No"

Me: "I'll tell your parents!"

Girl 2: "Grown ups can't come in"

Girl: "Let's let him do the code. You have three attempts"

The girl wrote on a board the number 10112, then asked me, "what do you see?". I said, "well, 10112". "Wrong!" she said, claiming I should have answered 11102112. "Let me try again", I said. She wrote 111. "Easy", I thought. "It's 111011". "NO!" she said, "it's 31". When I didn't believe her she asked some other kid that was passing by, and sure enough he confirmed her two answers. "I have a phone call", I said, to try and stall and see some answers before my final guess. Not to long though, recess is only 20 minutes.

Here's what I found:

  • 10112 -> 11102112
  • 111 -> 31
  • 123 -> 111213
  • 4400111 -> 242031

Everyone that solved this did so effortlessly, not wasting a second contemplating, as if the result was completely obvious. I was starting to wonder what kind of damage can such a group of child savants cause.

Suddenly, I was startled. "Dad! are you following me?!". A pair of angry eyes stared into my soul. "I told you not to come to my secrete place! Is this mom on the phone?"

She went and talked to her mom, and I knew it was my last chance. I sneaked back towards the board.

"Look closely", said the girl. "What do you see?"

Then she wrote


What do you see?

  • $\begingroup$ This sounds like exactly the kind of club I would create at school :P $\endgroup$
    – Zimonze
    Jul 29, 2018 at 20:00

1 Answer 1


I see



You express what you "see" in numbers. For example, 111 is 31 because you see "three ones" in the number 111. Similarly, 11023212 is "two ones, one zero, one two, one three, one two, one one, one two" or 21101213121112.


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