Zeroes and Ones - 30 points
Writeup by poortho
Problem Statement: Bit String Flicking
How many solutions are there for X in the expression:
LCIRC -3 (01011 AND X OR 10100) = 01101
Try simplifying it?
This problem is a simple bit string flicking equation. Let's begin.
First, LCIRC-3 means that you cycle the bits left 3 times. The inverse of LCIRC-3 is RCIRC-3, so we can rewrite the equation as
01011 AND X OR 10100 = 10101
Then, order of operations dictates that we perform the AND then the OR.
Thus, because the OR is applied last, we know that the 2nd and 4th bit of
01011 AND X has to be 0, the 5th bit has to be 1, and the 1st and 3rd bit can be anything.
So now we have
01011 AND X = ?0?01. Again, we see that the 1st and 3rd bit of X can be anything. We also see that the 5th bit has to be 1, and the 2nd and 4th bit must be 0.
Thus, our answer is 2^(number of ?'s) = 2^2 = 4, which is our flag.