When looking for the units digit of 3n, look at the value of mod(n,4). When this is 0, the units digit is 1, when it is 1 the units digit is 3, when it is 2 the units digit is 9, when it is 3 the units digit is 7.
mod(777,4) = 1, so the units digit of 3777 is 3.
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