5 super hard questions....

  1. Suppose we have n distinct lines on a plane. What is the maximum and minimum number of intersections?

  2. Suppose we have n distinct points on a plane. What is the maximum and minimum number of line that they can form?

  3. What is the maximum number of region that n lines can divide a plane into?

  4. Given n collinear points , what is the maximum and minimum distance between the points?

  5. Arrange seven points on a plane such that , for any 3 points , we can find 2 points with distance 1.

Note by Werjohi Khhun
4 years, 7 months ago

No vote yet
1 vote

  Easy Math Editor

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.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. 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 1

paragraph 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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

  1. Minimum=0, all lines are parallel.For maximum, no line must be parallel or concurrent. Now each of n lines intersects at 1 point. Thus, maximum number of intersections=(n2)\dbinom{n}{2}

  2. Minimum=1, all points are collinear. For maximum, assume all points on a circle, ie. no 3 of them are collinear, this will give again (n2)\dbinom{n}{2}

  3. This can be proved by recursion. See complete proof here

  4. Minimum=0+=0^+, maximum==\infty. Either I am not understanding it properly or its vague.

Pranjal Jain - 4 years, 7 months ago

Log in to reply

For 1 , 2 , how do u know that it is N 2 ?? And , can you please explain what's that……??

werjohi khhun - 4 years, 7 months ago

Log in to reply

How many ways are there to select 22 objects from NN given objects? That's (N2)\dbinom{N}{2}. Thus, in 1.1., I selected 22 lines out of nn to find number of intersections. Similarly, in 2.2., I selected 22 points out of nn points, to draw a line.

  • In general, (xy)\dbinom{x}{y} is the number of ways to select yy objects out of xx given objects. For more details, see this. I hope it helps.

  • Though if you don't know about Permutations as well, I'll recommend you to read a wiki on permuations from here first.

  • (N2)=N(N1)2\dbinom{N}{2}=\dfrac{N(N-1)}{2}

  • If you need some more help, feel free to either comment here or at Moderator's Messageboard here

Pranjal Jain - 4 years, 7 months ago

Log in to reply

@Pranjal Jain Oh , i never learnt about that tyep of permutations.... But why isit 2 ?? In what situation we can use 3,4 or 5 ?

Thank you.

werjohi khhun - 4 years, 7 months ago

Log in to reply

@Werjohi Khhun When you are supposed to select 33 objects out of NN objects, use 33.

Say, we are given 55 objects, (A,B,C,D,E)(A,B,C,D,E)

  • Number of ways to choose 22 objects:(52)=10\dbinom{5}{2}=10

{(A,B),(A,C),(A,D),(A,E),(B,C),(B,D),(B,E),(C,D),(C,E),(D,E)}

  • Number of ways to choose 44 objects:(54)=5\dbinom{5}{4}=5

{(A,B,C,D),(A,B,C,E),(A,B,D,E),(A,C,D,E),(B,C,D,E)}

  • Number of ways to select 55 objects:(55)=1\dbinom{5}{5}=1

{(A,B,C,D,E)}

Pranjal Jain - 4 years, 7 months ago

Log in to reply

Solution needed.

werjohi khhun - 4 years, 7 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...