Can you solve the Leonardo da Vinci riddle?  Tanya Khovanova

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Meet The Creators
 Educator Tanya Khovanova
 Director Outis
 Script Editor Alex Gendler
 Animator Nemanja Petrovic
 Associate Producer Bethany CutmoreScott, Elizabeth Cox
 Content Producer Gerta Xhelo
 Editorial Producer Alex Rosenthal
 Narrator Addison Anderson
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Interestingly, we can expand on autobiographical numbers. Consider this: if there is a notion of an autobiography of a number, then it would be logical to expect there to be a notion of a biography of a number. What would be the logical candidate for a biography of a number? Let us say that given a number N, its biography is another number M such that the first digit of M is the number of zeroes in N, the second digit of M is the number of ones in N and so on.
For example, it is possible to have two numbers that are biographies of each other: 130 and 1101. Can you find two 10digit numbers that are biographies of each other?
If you want to find out more about the biographies of numbers, check out the educator’s "A Story of Storytelling Numbers."
You can also explore the educator’s math blog here.
There are many interesting sequences that describe themselves. For example, the Golomb sequence, a(n), is lexicographically the earliest nondecreasing sequence of positive integers such that a(n) is the number of times that n occurs in the sequence. It has to start with 1: a(1) = 1. That means we have 1 one. Therefore, a(2) can't be 1. We pick the next smallest number available, so a(2) =2. Now we have to have 2 twos, so we need one more two. Thus a(3) = 2. The last equation says that the sequence has to have 2 threes. As we already used all ones and twos, we have a(4) = a(5) = 3. The first few terms of the sequence are:
1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12.
This sequence is sequence A001462 in the Online Encyclopedia of Integer Sequences.
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About TEDEd Originals
TEDEd Original lessons feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TEDEd original? Nominate yourself here »
Meet The Creators
 Educator Tanya Khovanova
 Director Outis
 Script Editor Alex Gendler
 Animator Nemanja Petrovic
 Associate Producer Bethany CutmoreScott, Elizabeth Cox
 Content Producer Gerta Xhelo
 Editorial Producer Alex Rosenthal
 Narrator Addison Anderson