Flipped Colour

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.
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