Dishes Problem- Analytical Approach

Hello Everyone!

So here is my analytical approach to this problem..

Since we have 2 guests sharing rice, 3 sharing broth and 4 sharing meat, we have think about where do they meet. What I mean by saying 'where do they meet' is that for the given scenario where there are 2+3+4= 9 total people and there are 3 dishes in total, if they rotate from one dish to other there will be 12 different combinations possible in this scenario.

To make it a little clear, please look at the following:

Multiples of 2 are: 2, 4, 6, 8, 12
Multiples of 3 are: 3, 6, 9, 12
Multiples of 4 are: 4, 8, 12

Therefore, we can see that they meet at 12.

Now, with total 12 possible combinations, 2 of them shared a bowl of rice therefore there has to be 12/2= 6 bowls of rice, 3 of them shared a bowl of broth therefore there has to be 12/3= 4 bowls of broth, and 4 of them shared a plate of meat therefore there has to be 12/4= 3 plates of meat in total.

Now you add the total number of rice bowls and broth bowls and plates of meat to find out the total number of dishes at the party:
that is- 6+4+3= 13

Now that we know that there are total number of 13 dishes with 12 people at the party.
However, we need to find number of people for 65 dishes at the party. This means 13*5 is 65, therefore, 12*5 is 60. Therefore, there is 60 total people at the party with 65 dishes present.

Cultural context has a mild effect on this problem; such as, when one is reading the problem they may get confused whether 2 guests sharing a rice bowl only eat rice or they also eat meat and broth too.