What is the maximum possible number of streets any one of which could be the one the crew cleaned on Friday afternoon?

AddisonPatton August 15, 2019

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I do not understand why 5 is the answer. Because if either 1 or 3 has to be cleaned on Monday morning, wouldn't that mean that there would be only 4 other possible streets left to clean on Friday afternoon? (5, 6, 2, and whichever one of 1 & 3 that wasn't cleaned on Monday morning)

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Irina August 16, 2019

@AddisonPatton,

The question asks which one of the following streets could be cleaned on Friday afternoon. We have determined the cleaning schedule for streets 8,4, and 7, thus, streets 1,2,3,5, and 6 are available. It is true 1 or 3 could go on M am but either 1 or 3 could also go on F pm, nothing in the rules tells us that only 1 or 3 could go on F pm. It is true that we cannot clean both streets 1 & 3 on F pm, but this rule applies to every street, it is one street per time slot. This question simply asks how many possible scenarios there are for the F pm time slot.

Let's illustrate all the possible scenarios for F pm:

am 1 4 3 7 X
pm 8 6 X 2 5
M T W Th F

am 1 4 3 7 X
pm 8 6 X 5 2
M T W Th F

am 1 4 6 7 X
pm 8 5 X 2 3
M T W Th F

am 3 4 6 7 X
pm 8 5 X 2 1
M T W Th F

am 1 4 3 7 X
pm 8 5 X 2 6
M T W Th F

These scenarios demonstrate that in a valid cleaning schedule, F pm slot could be occupied by the streets 1, 2, 3, 5 or 6.

Does this make sense?

Let me know if you have any further questions.

AddisonPatton August 16, 2019

Okay. That makes sense. Thank you.

Ravi August 16, 2019

@AddisonPatton, let us know if you have any other questions!