[zoky]

> The original argument was "the ones digit has permanent pattern in 2^n {2,4,8,6,2...}.

Isn’t that obviously the case (for n >= 1 anyway)? If each successive power of two is just the previous number times two, then it would always have to follow that pattern.

Any integer >= 10 can be expressed as the sum of a multiple of 10 plus a single digit number, for example 32 = 30 + 2. So 32 * 2 can be written as 2 * (30 + 2). And since any integer ending in zero multiplied by any integer must also end in zero, you only need to look at the single digit part of the number to see that a pattern must immediately emerge for powers of two, or of any number for that matter.