Difference between revisions of "2021 WSMO Speed Round/Problem 1"
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Revision as of 17:28, 22 December 2021
Problem
Let , and let
. Find the value of
.
Solution (bash)
Note that \begin{align*} |f^7(2)|&=f(f(f(f(f(f(f(2)))))))\\ &=f(f(f(f(f(f((2-1)^2))))))\\ &=f(f(f(f(f(f(1))))))\\ &=f(f(f(f(f((1-1)^2)))))\\ &=f(f(f(f(f(0)))))\\ &=f(f(f(f((0-1)^2))))\\ &=f(f(f(f(1))))\\ &=f(f(f((1-1)^2)))\\ &=f(f(f(0)))\\ &=f(f((0-1)^2))\\ &=f(f(1))\\ &=f((1-1)^2)\\ &=f(0)\\ &=(0-1)^2=\boxed{1} \end{align*}