For how many of the six new employees is the assignment of a parking space limited to one of only two possible spaces?

Jordan on July 17, 2018


Please explain how the correct answer is D instead of C.


Michelle on July 19, 2018

Hey @homework thanks for your question

Let's start with the variable R. The last rule states that R can only be in spaces 1, 2, 3, or 4. But because T and Y must both come before R, R cannot be in spaces 1 or 2. That leaves 3 and 4 as the only available spaces for R.

Now let's work on Y. Y must come before R, which can only be in space. 3 or 4. But Y must also come after T, so Y cannot be first. That only leaves spaces 2 or 3 available for Y.

Next let's look at T. T must come before Y, and Y can only occupy spots 2 or 3. That means spots 1 and 2 are the only spots available to T.

Finally, let's turn our attention to X. X must come after S. Because 3 out of the first 4 spots are always occupied by T, Y, and R, there is only ever one remaining spot available in 1-4. Placing X in any of the first four spots would leave no space for S to come before X. Therefore X must be in either spot 5 or 6.