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A Quick Puzzler from Perelman

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Edited by Richard Walker, Friday 16 October 2026 at 11:31

Another one from Perelman's book.

In each row A - C identify the expression with the largest and smallest values

A. 222 ,    two super 22 ,    two super two squared

B. 333 ,    three super 33 ,    three super three cubed

C. 444 ,    four super 44 ,    four super four super four

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Answers
A. two super two squared is only multirelation two super four equals 16 less than 222 so it is smallest. two super 22 is clearly bigger than 222 so it is largest.
B. 333 is less than three super three cubed equals three super 27 so it is smallest.  three super 33 is clearly bigger than three super 27 so it is the largest.
C. 444 is much less than the gigantic four super 44 , but this time the 'power tower' is the winner because four super four super four equals four super 256 , clearly greater than four super 44 .

In fact four super 256 is colossal: it equals

13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

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