I was going through a JSTSE paper, When I found this question...

How many points (x,y) exist in the 1st quadrant such that x+y=7 ?

Note by Mehul Arora
5 years, 7 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

If the number of points(x,y) are said to be only whole numbers(not decimals), then there are 6, they are:

$(1,6),(2,5),(3,4),(4,3),(5,2) and (6,2)$

If it is mentioned, including decimals, then it is infinite . . .

What do you say Azhaghu Roopesh M ???

- 5 years, 7 months ago

Yeah , since the number 7 is quite small , we can count it out .

- 5 years, 7 months ago

Exactly. Is there any formula for these kind of problems???

- 5 years, 7 months ago

Look up the Generating Functions wiki here on B'ant . Anyway , I've got to go now, Bye :)

- 5 years, 7 months ago

@Sravanth Chebrolu Do (0,7) and (7,0) not lie in any quadrant? Coz the definition of the point in the 1st quadrant is x,y>0. Anyways.. If included, they should be 8 in number , eh. I think there is a typo.

- 5 years, 7 months ago

Yeah it was a typo, I've changed it. And yes, I think what you said is also right, the points (7,0) and (0,7) lie on the axes not the quadrants.

- 5 years, 7 months ago

The formula for the number of Natural numbers satisfying $x + y = k$ is always $k-1$.
So in this case k = 7 . Hence number of points are 6

This formula is just a observation based. Please verify it @Azhaghu Roopesh M @Krishna Ar @Sravanth Chebrolu

- 5 years, 7 months ago

Yes, I too think the same, but if the no. of points asked is in fractions or decimals there can be many . . .

What do you say @Rajdeep Dhingra ???

- 5 years, 7 months ago

Well as this formula is valid only for natural numbers so the sum will also be a natural number.
If it is not specified natural number or k is a rational number with denominator $\ne$ 1 then the answer is $\infty$

- 5 years, 7 months ago

Exactly. Then this might have been included in the question . . .

- 5 years, 7 months ago

Is this the exact same question ? If so , it is a simple question of Generating Functions

- 5 years, 7 months ago

Generating functions? Are you sure? This is a JSTSE question, so its for classes 10 or below I think.

- 5 years, 7 months ago

Not exactly below.. The maths questions were mainly Of class 10 level iincluding all AP, GP , Quadratics, Vieta's etc...

- 5 years, 7 months ago

Well , I think any class 10 student has the ability to count the number of solutions manually , it's just that the method of Generating Functions works for finding solutions of the type :$x+y = N$ or other types .

- 5 years, 7 months ago

I guess there would have been more information provided. Most likely the question would have specified $x,y$ to be integers.

- 5 years, 7 months ago

But it has been said that x,y belong to the first quadrant , so automatically $x,y \geq 0$

- 5 years, 7 months ago