# Which one of the following could be the buildings owned by the three companies after only one trade is made?

Meredith on October 23, 2019

Speed

How do you do this game fast?

Irina on October 23, 2019

@Meredith,

This is a fairly challenging game so your target time should be in the 8-9 minute range or so. It is very open ended, so the key is to pay attention to the exchange rules. We can only exchange class 1 for 2x class 2, class 2 for 2x class 3, and each building can be exchanged with the building of the same class. Thus, if R owns 1 building of class 1 and 2 buildings of class 3, no matter how many exchanges they make they can never own 2 buildings of class 1, they can either own:
1x class 1 and 1x class 2
3x class 2, or
2 x class 2 and 2x class 3

Same with S they own 1 bldg of class 1 and one building of class 2, they also can never own two buildings of class 1. They could own:
- 1x class 1, 1x class 2
-3 x class 2
-2x class 2 and 2x class 3
-1x class 1 and 2x class 3

T has 3 buildings of class 2, so they also cannot own two buildings of class 1- no own can own two buildings of class 1 in this game, they could own:
-3x of class 2
-1x class 1, 1x class 2
-2x class 3, 2x class 2

This information is sufficient to answer questions 1,2. For question 3, it asks us if R owns only class 2 bldgs, which means they exchanged both their class 3 and class 1 building. Well, class 1 can only be exchange to 2x class 2, and T is the only company that has 2x class two, so it must be true that they traded with them. Hence, we can conclude that T must own a class 1 building.

For question 4, we are given a scenario where T owns no class 2 buildings. We know that they own 3x class 1 buildings, so they could only exchange them for 1x class 1 and 2x class 3 to end up with no class 2 buildings. The only class 3 buildings are Z Y , so T must own both of them.

For question 5, we are asked which of the following cannot be true/ must be false. We can look at the setup above to see that it is impossible for T to own 1 class 1 and 1 class 3 building - even if you did not write it out in the beginning, it is an easy inference to make if they start of with 3x class 2 buildings, hence they cannot possibly own F and Y.

This is a fairly unusual game and requires you to keep track of which building belongs to which class, but it is also open ended so the questions can be answered without checking on any additional rules aside from the exchange rate.

Let me know if this helps and if you have any other questions.