Find the $999^{th}$ digit (from the right, in base 10) of the number
\[ 5^{\left(4^{\left(3^2\right)}\right)}\]
Hint: use trunction, or integer division, mod, remainder; some people solved this
by converting the number to a string and extracting the character from the string.
Bonus: answer the same question for the expression:
\[ 2^{\left(3^{\left(4^5\right)}\right)}\]
Question #2:
Your answer should be an integer because this is the formula
for the number of tilings of an $10 \times 10$ grid with dominos.
The mathematical symbol $\prod$ represents
product or multiplication.
You do not need to hand this assignment, but I would like you to
introduce yourself and let me know how you did on it.
You may want to use the help function on following commands to get help on functions you will
need to compute these expressions:
irem, iquo, mod, trunc, convert, sqrt, cos, Pi, nops, ops, mul, evalf, simplify, Digits.