Heres a classic brainteaser that I dont like.
Whats the next number in this sequence: 1, 11, 21, 1211, 111221, …?
The answer is 312211, because each number describes the digits in the number that precedes it.
one one, i.e.
The next entry describes 11 as two ones, or 21.
This, in turn, is one two followed by one one, or 1211, and so on.
Legendary mathematician John Conway studied this so-called look-and-say sequence and actually proved some interesting results about it.
Conway also studied the sequences that spring from different starting numbers other than 1.
Determining which one is your bonus puzzle this week.
My gripe with sequence puzzles is that theyre open to multiple possible solutions.
Your main puzzle this week concerns a number that describes itself.
And rest assured it has only one solution.
Did you miss last weeks puzzle?
Check it outhere, and find its solution at the bottom of todays article.
Be careful not to read too far ahead if you havent solved last weeks yet!
Puzzle #39: A Self-Referential Number
Only one 10-digit number has the following property.
Numbers cant begin with a zero.
An example of a four-digit number with this property is 2020.
Bonus: you could seed the look-and-say sequence with any whole number.
Conway proved that all seeds yield a sequence whose entries grow to infinity, with only one exception.
Ill be back next Monday with the solutions and a new puzzle.
Do you know a cool puzzle that you think should be featured here?
it’s possible for you to only ever take at most one prime numbered paycheck throughout the whole game.
So our approach cannot be improved.
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