Alice wants Chris--a mischievous little boy--to deliver a message to Bob which consists of 7 squares, numbered 1 through 7 from left to right and colored either red or white. As expected, Chris switches the color of exactly one of the 7 squares in the original message and thus Bob receives the following message:
Alice knew beforehand that Chris would play this trick, so she had already told Bob the following information on the original message:
- Squares numbered \(1,3,5,7\) have an odd number of red squares.
- Squares numbered \(2,3,6,7\) have an even number of red squares.
- Squares numbered \(4,5,6,7\) have an odd number of red squares.
Which is the original message Alice wanted to send?
Details and assumptions:
- The options are expressed as binary numbers: \(1\) represents a red square and \(0\) represents a white square.