Another one from Perelman's book.
In each row A - C identify the expression with the largest and smallest values
A. , ,
B. , ,
C. , ,
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Answers
A. is only so it is smallest. is clearly bigger than so it is largest.
B. is less than so it is smallest. is clearly bigger than so it is the largest.
C. is much less than the gigantic , but this time the 'power tower' is the winner because , clearly greater than .
In fact is colossal: it equals
13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
Tags: Algebra Can Be Fun, Power Tower, Yakov Perelman