Find the one's digit of 3 to the 200th power?

Ans: 1 Reason is that the last digit forms a repeated pattern. For 3^n, last digits are 3, 9, 7, 1 for n = 1,2,3,4. First repeated sequence goes from n= 1 to 4 Second repeated sequence goes from n= 5 to 12 50 th repeated sequence is 197, 198, 199, 200 To generalize this problem further: n th repeated sequence of "x" numbers goes from n*x-3, n*x-2, n*x-1, n*x See discussion page for additional thoughts.