# Math professor and number of rooms

• quark
In summary, the math professor stayed in room 204 on a floor with 288 rooms. The total number of rooms on the floor is 288 and the professor's room number can be found by solving for n in the equation n*(n+1)/2 = 204. It is also possible to simplify the problem by looking for numbers n for which sqrt((n * n + n) / 2) is an integer.
quark
A math professor was staying in a hotel before attending a math conference. When he came out of his room, to go to the conference, he found out that the total of room numbers to his left was equal to the total of room numbers to his right. The total numbers of rooms per floor were about 300 and just assume that they are in line. The room numbers were given without skipping any number(even 13 :rofl: )

How many rooms are there in the hotel floor and in which room did the professor stay?

It is damn easy solving with any of the computer programs. I did it in VB and excel(Also without these programs. By saying this I am not acting smart but just encouraging you guys). But there is a clue for getting the numbers by which you can skip all unnecessary numbers. Go get it.

Answer for the first floor (whited out)

There are 288 rooms on the floor. The professor is in room 204.
The sum of numbers of the first 203 rooms is
(203 * 204) / 2 = 20706.
The sum of numbers of the last 84 rooms is
(288 * 289) / 2 - (204 * 205) / 2 = 20706.

I looked for numbers n for which sqrt ((n * n + n) / 2) is an integer.

I don't have a solution for the second floor and higher.

Jimmy, you got it. The redundant data like, rooms in same floor and all in a line, actually takes care of all silly quesions. Try to further simplify the thing(I believe you can do it and you can cross check it with the whited out logic).

Further simplification results in n*(n+1)/2. So, either n and (n+1)/2 or n/2 and (n+1) should be perfect squares. If you start squaring numbers and check the above possibilities, you need not go morethan 17 trials.

## 1. What is a math professor?

A math professor is a person who teaches mathematics at a college or university level. They typically hold advanced degrees in mathematics and have expertise in a specific branch of math, such as calculus, algebra, or statistics.

## 2. What is the role of a math professor?

The role of a math professor is to teach students the principles and concepts of mathematics, as well as to conduct research in their area of expertise. They also grade assignments and exams, advise students, and may serve on committees within their department.

## 3. How many rooms does a math professor typically have?

The number of rooms a math professor has can vary depending on their specific job and personal preferences. Some may have an office for teaching and research, while others may also have a separate office for administrative tasks. Additionally, some professors may have access to a laboratory or other specialized rooms for their research.

## 4. What factors may influence the number of rooms a math professor has?

The number of rooms a math professor has may be influenced by factors such as the size and prestige of their university, their department's budget, and their own seniority and job responsibilities. Additionally, the type of research they conduct and the equipment and resources needed for it may also play a role in the number of rooms they have access to.

## 5. What is the significance of the number of rooms for a math professor?

The number of rooms a math professor has can impact their ability to effectively teach and conduct research. Having a dedicated space for each task can improve organization and productivity. Additionally, the number of rooms a professor has can also indicate their level of seniority and the resources available to them for their work.

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