Discussion: This student is close to a solution but is not quite there. It is recognized as an invariance type problem and the solution attempts to show that no matter how the coins are flipped something remains the same whereas this invariant is different for the desired endstate. Here the student assigns a value of 0 o a head (up) and a 1 to a tail (up). The original state is 0 (modulo 2) and the desired state is 1 (modulo 2). The student make the claim that the difference is always a multiple of 4 which would yield the result but this is incorrect and comes from inducting from the intial state. Had the student analyzed at any point the state of the four coins being flipped this would yield that the total number of heads changes by one of -4, -2, 0, 2, 4 and so there is always an odd number of heads and an even number of tails.

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