Member • Feb 21, 2008
Tough Puzzle: The Parrot Sequence - crack it!
The parrot sequence
Gaston owns a clever parrot called Paco which can describe out loud numbers read from a piece of paper displayed in front of him. One day
Gaston tried this funny experiment: he wrote the digit 1 on a sheet and showed it to Paco, who answered âone 1â. Gaston wrote down the parrotâs answer âone 1â or â11â on a new sheet and showed it to Paco, who readily answered âtwo 1âsâ. Again, Gaston wrote down his reply âtwo 1âsâ or â21â on another sheet and showed it to Paco, who replied âone 2, one 1â or â1211â... Gaston continued this experiment until he obtained a long sequence of numbers 1, 11, 21, 1211, 111221, 312211, etc... in which each next term is obtained by describing the previous term.
Can you say how many sheets of paper Gaston will need until:
a) the string of digits 333 appears, or
b) the digit 4 occurs in the sequence?
Can you also confirm that the last digit of any term of the parrot sequence is always 1?