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The number that it describes a yes mismo

Numerical territoryLevel 2/5

It seems like a numerical oddity, and it is; but not in the capricious sense. It has that special grace of problems in which each figure imposes conditions on all the others.

Search for a 10 digit number \[
d_0\ d_1\ d_2\ d_3\ d_4\ d_5\ d_6\ d_7\ d_8\ d_9
\] with this property: - \(d_0\) indicates how many zeros the number contains;

  • \(d_1\) indicates how many ones it contains;
  • \(d_2\) indicates how many twos it contains;
  • and so on;
  • \(d_9\) indicates how many nines it contains. What is that number?
Solve this riddle

Hints

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  1. The sum of all the cifras must ser 10, because cuentan the ten positions of the propio number.
  2. Many large figures cannot appear: almost all the weight is concentrated in a few positions.
  3. Start by deciding how many zeros there should be; That drags down almost everything else.

Solution

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The number is: 6210001000 Let's check it: - contains 6 zeros;

  • contains 2 ones;
  • contains 1 two;
  • contains 0 threes;
  • contains 0 fours;
  • contains 0 fives;
  • contains 1 six;
  • contains 0 sevens;
  • contains 0 eights;
  • contains 0 nines. That matches your own figures exactly:

6, 2, 1, 0, 0, 0, 1, 0, 0, 0 So 6210001000 is, in base 10, the autobiographical number sought.

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