Home > math puzzle > Puzzle on the road – how many combinations of food that I can have ?

Puzzle on the road – how many combinations of food that I can have ?

Let me start with the introduction of why I come up with this puzzle. I was invited to go to Trieste, Italy for a summer school in ICTP (click here for information of ICTP). I was lucky cause ICTP sponsored me so I did not have to pay for my living cost while I was there. Everyday, I ate in a cafeteria and I did not need to pay, cause ICTP gave me coupons that I can use to buy my lunch and my dinner. Cafeteria usually provides a set of first course meal, which is usually a pasta, a set of second course meal which is usually either beef, chicken, fish or vegetarian meal and a set of cooked vegetable.

One full meal that I can buy with a coupon,  consists of one of the first courses, one of the second courses and two of the cooked vegetables. In the first course meal, there are three choices of pasta and I am only allowed to take one of these. In the second course meal, there are also three choices  whether you want, say beef or fish or vegetarian meal and again I am allowed to take one of these. In the set of vegetable, there are three choices and I am allowed to take two of these three choices.

The question is how many combinations of meal that I can have.

To make it more interesting, let us assume that these following situations can occur.  I am sometimes so hungry so I take the full meal. But there is another time when I do not feel like eating so I do not eat. There is also another time when I want to eat but actually I am not that hungry so I only choose the first course and one of the cooked vegetable.

Anyway, it was a nice experience for me to be able to visit ICTP. I made a lot of friends for different countries there. I gained a lot of information that is really really useful for my research.

Here is a picture taken from my cell phone while I was there.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ps. I am not sure what is the correct answer. I have had already a number in my mind and let us confirm whether my guess is correct.

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