Lesson 4 Game 8

[kim4956]

Hi,

So I just reviewed Game 8 in the Lesson 4 Homework. The rules are pretty straightforward, but when you apply them to the question, you end up getting more than one possible answer (at least, that's what I keep getting!). To illustrate my point, let's say we're working on Q18.

"If exactly two paintings are oils and exactly two paintings are 19th-century paintings, which of the following must be true?"

The answer key says since there are exactly two oils, they must be either 2 and 3 or 3 and 6. But aren't there other possibilities, too? Are the possibilities restricted to 2 and 3, and 3 and 6 because there are exactly two paintings? That seems to be the only explanation, but I'm wondering if there's a simpler way to understand and apply these rules...

Thanks!
Kim

[Ladan Soleimani]

Hi Kim,

This game can be tricky because there isn't anything to place at the beginning. You are right that there are a lot of possibilities at the start.

The reason that the possibilities are limited, say for question 20, is because of the local rule it gives. If exactly two of the paintings are oils and exactly two are 19th century, then there are more restrictions since all the types of paintings (O and W) and the centuries (19 and 20) must be next to or above/below another painting of the same type (rules 2, 3, and 5). Since painting 3 is an oil, we always know that either painting 2 or painting 6 is an oil, or both. With the local rule telling us that only two paintings are oils, we know only one of 2 and 6 is an oil and everything else must be a watercolor. So 1, 4, and 5 are definitely watercolors and one of 2 and 6 will be a watercolor and one will be an oil.

We can then do the same thing for the century. Painting 2 is 19th century so either painting 1 or 3 must also be 19th century, since painting 5 below is 20th century. With only 2 being 19th century, the others will have to be 20th century. So paintings 4, 5, and 6 will be 20th century and one of 1 and 3 will be 19th century and one will be 20th century.

You are asked to find which answer must be false, or cannot be true. Answer choice (E) cannot be true because it has painting 4 as a 19th century painting. If painting 4 was 19th century then that would be the only other 19th century painting other than painting 2 and then neither of the two 19th century paintings would be next to or above/below the other, violating the fifth rule.

I hope this helps!
Ladan

[kim4956]

Thanks!