# If the cargo bed is cleaned exactly twice, which one of the following must be true?

Jessica-Killeen on January 22, 2019

How did you know

How did you know that those 7 configurations were the only 7 that would work? How did you decide on them? Isn't this method extremely time consuming? How did you know there aren't more than 7 configurations without wasting a ton of time trying them out?

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Jessica-Killeen on January 24, 2019

Ravi on February 13, 2019

@Jessica-Killeen,

Happy to help!

We know that those 7 configurations are the only 7 that can exist
because of our 2 rules:

1) Max 3 cleanings
2) M in 5

_ _ _ _ M _ _

The most important inference to draw in this game is that if there are
3 M pieces and 4 S pieces AND we can only have a maximum of 3
cleanings, then the M pieces cannot be spaced out individually because
if they were (as in, if they were in 1, 3, 5, and 7), then there would
be way too many cleanings.

From this, we know that the M pieces need to either go in a block
(MMM) or in a block of two and a single (MM with the the other M
somewhere).

You're right, this inference can take some time, but the benefit of
figuring it out and creating those boards is that the questions will
go by very fast.

We can answer this question without making all the different
scenarios. Let's see how that looks.

The question asks, "if the cargo bed is cleaned exactly twice, which
one of the following must be true?"

If there are two cleanings, then we know that there must be three
separate clusters of loads.

know there are only 2 cleanings, we cannot have two groups of M
clusters because that would require a minimum of three clusters. In
other words, we can't have MM and M somewhere else. Thus, we now know
that the Ms all have to be together.

What's more, we know the Ms can't go in 5 through 7 because if they
did, then there would only be 1 cleaning.

From this, we know the Ms are either in 3 through 5 or 4 through 6.

_ _ M M M _ _

_ _ _ M M M _

(A) says that "the second load is stone." We know this must be true
given that we've placed all of the Ms already in this scenario (with
two cleanings), so yes, the second load must be stone. (A) is the