Problems ahead, solve them.

There is a well-known test for divisibility by powers of 2: to check the divisibility of a number M by 2n, we form a new number M' using only the last n digits of M and then examine the divisibility of that number (i.e., M') by 2n. The test works because of the easily-proved fact that M is divisible by 2 if and only if M' is divisible by 2n.

Here are some problems for students in Senior School. Also find the solutions for the problems in the July 2014 issue of AtRiA.


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