## 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.

## (Another) Birthday problem puzzle

I’d like to discuss one of many birthday problem math puzzles. The complete puzzle and the solution can be found here. But let me write the puzzle as follows.

You and your colleagues know that your boss

A’s birthday is one of the following 10 dates:Mar 4, Mar 5, Mar 8

Jun 4, Jun 7

Sep 1, Sep 5

Dec 1, Dec 2, Dec 8

Atold you only the month of his birthday, and told your colleagueConly the day. After that, you first said: “I don’t knowA’s birthday;Cdoesn’t know it either.” After hearing what you said,Creplied: “I didn’t knowA’s birthday, but now I know it.” You smiled and said: “Now I know it, too.” After looking at the 10 dates and hearing your comments, your administrative assistant wrote downA’s birthday without asking any questions. So what did the assistant write?

When I first read this puzzle, I am confused. Let me just name the reader/myself “B” in the puzzle above to avoid more confusion. This puzzle is written in some way that the reader is part of the story. Hence the reader, B, was told the month of A’s birthday but we as the reader do not know the month of A’s birthday. Perhaps it is just a part of puzzle that we have to solve, therefore it might not be a big deal.

However, the big deal is the fact that the solution that I found is different from the solution given. I thought I might get wrong, therefore I look for the solution. What happened was I could not understand the solution. I thought it is just me but it turns out there is someone else who has the same experience.

I would like to modify a little bit of the puzzle in order to make this puzzle a bit clearer, well at least for me.

A’s birthday is one of the following 10 dates:Mar 4, Mar 5, Mar 8

Jun 4, Jun 7

Sep 1, Sep 5

Dec 1, Dec 2, Dec 8

We then have the following conversations between A’s friend.

C said: “I don’t knowA’s birthday, but I know only the day (the date) of A’s birthday,”

B said: “Well, I know only the month A’s birthday.”

C said: “Now I know it.”

B said: “Now I know it, too.”From the information given above, can you tell what is A’s birthday?

Perhaps, this version is better than the previous one. What do you think?

## Merry Christmas

Wishing you a very merry Christmas and a wonderful new year ahead.

Hoping you get your new year’s resolutions, a healthy life and many more.

Happy christmas..

ivanky

1. This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen. The sum of Jack’s age and three times Jen’s age is 66. How old is Jen?

2. One of your friends is heading north for the Christmas holiday and the other friend is heading south. If their destinies are 1029 miles apart and one car is traveling at 45 miles per hour and the other car is traveling at 53 miles per hour. How many hours before the two cars pass each other?

3. This Christmas we decided to buy some sweets and give those sweets to the children in the orphanage. If we gave each child 8 sweets then we would have 30 sweets left. If we gave the child 12 sweets each then we would have needed to boy 30 sweets more. Find the number of children in the orphanage?

4. This Christmas, my parents gave us a lot of candy canes. They gave all of those candy canes to my elder sister to distribute it. She then took some and gave me 2/3 of all candy canes. I kept 1/3 of the candy canes I had and gave the rest to my little brother. My brother ate 1/4 of the candy canes he had and gave the last 12 to my parents. How many candy canes did my little brother eat?

## Your says