Real Mathematics: Numbers #7

Self-Aware Numbers

There are some numbers that are special. Although Sometimes a bored mathematician could specify a few rules and give away definitions. And this is how world would have new special numbers.

Self-aware numbers are like that. It doesn’t matter if they have any use or not, there are self-aware numbers.

How to find them?

When you have a number, take a closer look at each digit. The digit that is at the left end gives us the number of zeros that exist in the number. Next digit gives us the number of ones, and the one on its right gives us the number of twos etc.


If such a number exists, we call them “self-aware numbers”.

Example 1:

1210 is a self-aware number. Let me break it down into its digits and we get:

1 = # of zeros,

2 = # of ones,

1 = # of twos,

0 = # of threes.

Since they are all correct, 1210 is a self-aware number. Good for you 1210!

Example 2:

10 is not a self-aware number.


1 = # of zeros, which is correct.

0 = # of ones, which should have been one!

10 is a bad number… Shame on you 10.

Example 3:

How about 141110; is it self-aware?

1 = # of zeros. Correct.

4 = # of ones. Correct as well.

1 = # of twos. There is no two in the number. Which makes 141110 not a self-aware number. You are bad 141110.


Select and Eliminate

Let’s assume that we have a square full of numbers like the following:


  1. Select a number. After circling it, eliminate all the other numbers which stay in the same column and row with the number you selected.

  2. Select another number from the remainders. Circle it and repeat the same process.

  3. Now select a third number from the survivors. Circle and repeat the process.

  4. You’ll see one number remained. Circle it too.
  5. Sum of the numbers you circled gives you exactly 10.

Better check it

  • Are there any self-aware 10-digit numbers?
  • Analyze the square from Select and Eliminate. Is there a specific algorithm for the numbers inside the square?

M. Serkan Kalaycıoğlu


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