^m^ is equal to the digits in positive integer m in reverse order, discounting the zeroes (e.g. ^41^ = 14 but ^3500^ = 53). Which of the following must be true? Select all that apply.

In this question seems better to plug in values to reach the correct answer, and since question asks for "must be true", we should work to falsify the options and the answer remaining will be our correct answer

A. ^m^ < ^m+1^
Lets consider m= 29 , thus m+1 = 30 , now ^m^ = 92 and ^m+1^ =3 , which means ^m^ > ^m+1^, thus this option is falsified.
B. m = ^(^m^)^
Easy one to eliminate , lets consider m=2500, thus ^m^ = 52 and ^(^m^)^ = 25 , thus m not equal ^(^m^)^ . Eliminate
C. ^1000m^ = ^m^ --> Here if we take any +ve integer , this condition satisfies , lets test with m=10, 1000m = 10000 and ^1000m^ = 1 and ^m^ = 1 , thus this condition will always hold true
D. (^m^)(^m^) > ^m^
Lets take m=10 , so ^m^ = 1 and (^m^)(^m^) = (1)(1) = 1 , thus this condition is also falsified, eliminate
Answer C.

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