If all of the nineteenth–century paintings are watercolors, which one of the following must be true?

Gabriela on May 7, 2018

Can you please show the game setup and question explanations

Can you please show the game setup and question explanations

7 Replies

Christopher on May 7, 2018

This is a multi-linear game, so there are two categories of information to track. First is Oil or Watercolor, and second is 19th or 20th. For a question like this, I would set up the problem visually like this:

_ _ _ _ _ _
1 2 3
_ _ _ _ _ _
4 5 6

Then fill in what you know:

_ _ _ 19 O _
1 2 3
_ _ _ 20 _ _
4 5 6

Then start applying rules to each question. The rules have a distinct patter that's fairly easy to check and test hypotheticals. Essentially, any painting must be vertically or horizontally adjacent to at least one other painting from the same century and of the same medium.

Question 1 gives the additional condition that all 19th century paintings are watercolors. Once we plug that into our scenario, then #2 must be a Watercolor. Given that #3 is Oil and must border at least one other oil painting, then #6 must be oil. Since all 19th century paintings are Watercolor, #3 and #6 must be 20th century paintings. #1 must be 19th Century so that #2 has an appropriate neighbor and Watercolor because all 19th Century paintings are. You can't tell anything about #4. 5 could be either Oil or Watercolor because while all 19th Century paintings are Watercolor, that does not mean that all Watercolor paintings are 19th Century.

W 19 W 19 O 20
1 2 3
__ __ 20 O 20
4 5 6

So looking at the options, A is false, B is false, C is unknown, D is unknown, E must be true.

Christopher on May 7, 2018

With the same basic setup, question 2 asks you to identify which two paintings could be the two Watercolors if there were 4 Oils and 2 Watercolors.

_ _ _ 19 O _
1 2 3
_ _ _ 20 _ _
4 5 6

This one just takes remembering the rules and looking at the setup. If we are looking for only two Watercolor paintings, they MUST border each other vertically or horizontally. Answer D is the only one that does that. The others can all be immediately eliminated just by looking to see if they border each other.

Christopher on May 7, 2018

@GPulla question 3 adds the constraint that there are exactly 3 of each Oil and Watercolor (you can disregard all Century logic). Since each Oil and each Watercolor must touch the other paintings of the same medium and #3 is established as an Oil painting, you have limited options.

O _ O 19 O _
1 2 3
W _ W 20 W _
4 5 6

W _ O 19 O _
1 2 3
W _ W 20 O _
4 5 6

W _ W 19 O _
1 2 3
W _ O 20 O _
4 5 6

In those three scenarios, the only thing that stays consistent is that #4 is a Watercolor. Paintings #1, #2, #5, and #6 could all be either Oil or Watercolor.

Christopher on May 7, 2018

@GPulla question 4 adds the constraints that exactly two paintings are Oil and two are 19th Century. Looking back at our basic scenario, there are a few things that we can easily see. Either #2 or #6 will need to be Oil and only #2 or #6 CAN be Oil. Also, either #1 or #3 will need to be 19th Century and only #1 or #3 CAN be 19th Century.

_ _ _ 19 O _
1 2 3
_ _ _ 20 _ _
4 5 6

So the question asks for the answer that must be false. (E) says has #4 as a 19th Century painting which does not border #2 and so could not possibly be one of the two 19th Century paintings and therefore must be false.

Christopher on May 7, 2018

@GPulla question 5 can be solved through process of elimination.

_ _ _ 19 O _
1 2 3
_ _ _ 20 _ _
4 5 6

B, C, and D are essentially the same answer and break down for the same reason. If you only have three of any type of painting, you can not have bordering paintings all the way from corner to corner. It would take four paintings to reach from #1 to #6 (either #1, #2, #3, #6 or #1, #4, #5, #6) or from #3 to #4.

E would be possible except that #5 must be 20th Century. Having #2, #4 and #6 as 19th Century paintings would mean that none of the paintings border paintings from the same century as prescribed.

That leaves A, which works. #5 is already 20th Century, so #1 and #4 fit the constraints.

Gabriela on May 16, 2018

Thank you!

on August 22, 2018

The answers in the book say that D is the correct answer for the first question on this game, but it is certainly not. I'm concerned that there are other discrepancies throughout the book and that I may be studying wrong answers