# Country and Its Capital

Five Managers - K, M, N, O and P - visited five Countries, F, A, B, G and K, such that each manager visited exactly four Countries. Further, each Country has a different capital city from among Merine, Colnia, Prine, Tomato and WaltC. Any person who visited a Country visited its capital city.

It is also known that:

• For any pair of managers, the number of Countries that both of them visited was at most three.
• N visited G, but did not visit Prine, while both K and O visited Tomato.
• O visited F, whose capital city is not Prine, while the capital city of B is not WaltC.
• Both K and P visited WaltC, while both M and N visited B.
• P visited Tomato, but he did not visit K the capital city of which is not Colnia.

Source : Me

Which Country did K not visit? A ,F , B , Cannot be determined

Pls tell the approach.

K did not visit:

B

Solution:

1) P did not visit K, this means he must have visited every other country
2) K cannot be Walt C, Tomato or Colnia. K cannot also be Prine because if K were Prine, N and P would've visited all the same countries. This means that Prine is the capital of A, Merine is the capital of K and N visited F, B, G, K.
3) From here we know that O, K and M all visited both A and K because if they visited neither of them they would've visited the same countries as either N or P.
4) If you assume that O did not visit G, the matrix resolves to K didn't visit B with all information being correct. However, if you assume that O did not visit B, a 50/50 occurs where K or M both may not have visited F or G, however in both these scenarios K will need to either have not visited either Walt C or Tomato, which is impossible as stated in the question.

Visualization of part 4:

Starting:

Correct Assumption:

50/50 Chance after incorrect assumption:

Both Outcomes to the incorrect:

• Can you pls elaborate on (4) ? I didnt understand that part...
– sam
Commented Oct 22, 2018 at 14:51
• @sam I've added pictures to illustrate part 4 Commented Oct 23, 2018 at 4:48