Wednesday, February 12, 2014

26: The Units Digit

Let's play "Spot the Pattern" !

What is the units digit of $3^{3^{3^{3}}}$ ?


4 comments:

  1. My TI-89 tells me the answer is a sideways 8. What does that mean? Is this thing broken?

    ReplyDelete
  2. You got to figure out the pattern:
    3^1 =3,
    3^2 = 9,
    3^3 = 27
    3^4 = 81
    3^5 =243
    units digit goes 3, 9, 7, 1, 3, ...
    So, how many groups of four is that?

    ReplyDelete
  3. It is 3^ 27 which would end in 7, no?

    ReplyDelete
  4. it's 3^(3^3^3), which can be rewritten as 3^(27^3).
    27^3 = 19683
    and 19683 / 4 = 4920.75 OR 19683 mod 4 = 3

    Either way of thinking gets you that we're at the third spot in the cycle, units digit is 7.

    ReplyDelete