In a school of $800$ students, $224$ students play cricket, $240$ students play

by Vulch, Apr 20, 2025, 11:41 PM

Hello everyone,
In a school of $800$ students, $224$ students play cricket, $240$ students play hockey and $336$ students play basketball. $64$ students play both basketball and hockey, $80$ students play both cricket and basketball, $40$ students play both cricket and hockey, and $24$ students play all three: basketball, hockey, and cricket. Find the number of students who do not play any game.

Edit:
In the above problem,I just want to know that why the number of students who don't play any game shouldn't be 0, because,if we add 224,240 and 336 it comes out to be 800.I have solution,but I just want to know how to explain it without theoretically.Thank you!

This post has been edited 1 time. Last edited by Vulch, 5 hours ago

100th post

by MathJedi108, Apr 20, 2025, 10:59 PM

Well I guess this is my 100th post, it would be really funny if it isn't can yall share your favorite experience on AoPS here?

100th Post

Median geometry

by Sedro, Apr 20, 2025, 6:03 PM

In triangle $ABC$ , points $D$ , $E$ , and $F$ are the midpoints of sides $BC$ , $CA$ , and $AB$ , respectively. Prove that the area of the triangle with side lengths $AD$ , $BE$ , and $CF$ has area $\tfrac{3}{4}[ABC]$ .

geometry

median

geometry

by carvaan, Apr 20, 2025, 5:48 PM

OABC is a trapezium with OC // AB and ∠AOB = 37°. Furthermore, A, B, C all lie on the circumference of a circle centred at O. The perpendicular bisector of OC meets AC at D. If ∠ABD = x°, find last 2 digit of 100x.

geometry

Angle Chasing

geometry

by carvaan, Apr 20, 2025, 5:46 PM

The difference between two angles of a triangle is 24°. All angles are numerically double digits. Find the number of possible values of the third angle.

geometry

Angle Chasing

Graph of polynomials

by Ecrin_eren, Apr 20, 2025, 3:00 PM

The graph of the quadratic polynomial with real coefficients y = px^2 + qx + r, called G1, intersects the graph of the polynomial y = x^2, called G2, at points A and B. The lines tangent to G2 at points A and B intersect at point C. It is known that point C lies on G1. What is the value of p?

This post has been edited 1 time. Last edited by Ecrin_eren, Yesterday at 8:30 PM
Reason: Mb

algebra

polynomial

Combinatorial proof

by MathBot101101, Apr 20, 2025, 7:37 AM

Is there a way to prove
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}
without induction and using only combinatorial arguments?

Induction proof wasn't quite as pleasing for me.

combinatorics

Combinatorial Proof

Recursion

by Sid-darth-vater, Apr 20, 2025, 3:02 AM

Help, I can't characterize ts and I dunno what to do

Attachments:

weird permutation problem

by Sedro, Apr 20, 2025, 2:09 AM

Let $\sigma$ be a permutation of $1,2,3,4,5,6,7$ such that there are exactly $7$ ordered pairs of integers $(a,b)$ satisfying $1\le a < b \le 7$ and $\sigma(a) < \sigma(b)$ . How many possible $\sigma$ exist?

Find all triples

by pedronis, Apr 19, 2025, 12:14 AM

Find all triples of positive integers $(n, r, s)$ such that $n^2 + n + 1$ divides $n^r + n^s + 1$ .

This post has been edited 2 times. Last edited by pedronis, Apr 19, 2025, 12:16 AM

Divisibility

Submit

I still exist as well.
by G.G.Otto, Aug 11, 2023, 2:44 AM
hello I'm still here lol
by player01, Aug 6, 2022, 6:24 PM
[REVIVAL] I will start posting more calculator relating posts very soon. Even though school has been busy, I have been programming my calculators a decent amount, so I have a lot to share...
by sonone, Feb 18, 2022, 10:29 PM
wow its been like 2.5 years since geo class
by pieMax2713, Feb 4, 2022, 8:38 PM
@violin21, I've been very busy with school lately and haven't been able to add another lesson. I will when i get a free moment
by sonone, Aug 19, 2021, 12:45 AM
ORZ CODER
by samrocksnature, Aug 9, 2021, 9:57 PM
Could you make more Asymptote lessons on your "How to do Asymptote" blog?
by violin21, Aug 9, 2021, 7:26 PM
You can take it, just C&P the CSS into your CSS area
by sonone, Apr 17, 2021, 10:08 PM
how can we take the CSS if we have permission to not take it?
by GoogleNebula, Apr 17, 2021, 5:22 PM
That is awesome!
by sonone, Apr 15, 2021, 10:09 PM
I modified your dodecahedron and got:
[asy]
import three;
import solids;
size(300);
currentprojection=orthographic(0,1.3,1.2);
light(0,5,10);

real phi=(sqrt(6)+1)/3;
real g=(phi-1)/2;
real s=1/2;
real a=sqrt(1-phi*phi/4-g*g)+phi/2;

triple[] d;
d[0]=(phi
by Andrew2019, Mar 26, 2021, 12:15 AM
Not too many, just changing the color here and there. I really like your CSS!
by sonone, Feb 2, 2021, 10:35 AM
Nice!

I see you're making changes to the CSS.
by G.G.Otto, Feb 1, 2021, 9:26 PM
I'm learning Java now!
by sonone, Feb 1, 2021, 5:56 PM
And I took part of it from CaptainFlint and then added a ton of modifications.
by G.G.Otto, Dec 1, 2020, 8:56 AM
fixed $\text{[math]}$
by sonone, Apr 25, 2020, 8:43 PM
Change in progress...
by sonone, Apr 25, 2020, 8:42 PM
When it says "At least 11 users clicked that button" it's incorrect since one person could have just posted 11 times. It should say "At most 11 users click that button".
by G.G.Otto, Apr 25, 2020, 8:26 PM
see this PM
by sonone, Apr 25, 2020, 7:03 PM
I can't get the cursor to work.
by G.G.Otto, Apr 25, 2020, 6:38 PM
If the cursor is confusing, where you are actually pointing in a front of the ship
by sonone, Apr 25, 2020, 11:04 AM
It's ok $\text{[math]}$
by sonone, Apr 23, 2020, 5:30 PM
Sorry I haven't been posting. I've got a Research Paper (for Roman History) due in a week.
by G.G.Otto, Apr 22, 2020, 11:15 PM
You should download it, as it's really useful when learning python. You can find out more here
by G.G.Otto, Apr 19, 2020, 10:04 PM
No. I don't have IDLE.
by sonone, Apr 18, 2020, 7:49 PM
Do you have IDLE installed on your computer? If so, I can give you a couple really cool codes that made that don't work in the AoPS widgets.
by G.G.Otto, Apr 14, 2020, 6:47 AM
I don't know how to change it....
by G.G.Otto, Apr 5, 2020, 5:58 PM
Do you know how the change the into thing above my avatar a different color? It's too hard to see.
by sonone, Apr 5, 2020, 2:08 PM
WELCOME TO MY BLOG!
by sonone, Mar 31, 2020, 4:56 PM

98 shouts

sonone's place

by Vulch, Apr 20, 2025, 11:41 PM

by MathJedi108, Apr 20, 2025, 10:59 PM

by Sedro, Apr 20, 2025, 6:03 PM

by carvaan, Apr 20, 2025, 5:48 PM

by carvaan, Apr 20, 2025, 5:46 PM

by Ecrin_eren, Apr 20, 2025, 3:00 PM

by MathBot101101, Apr 20, 2025, 7:37 AM

by Sid-darth-vater, Apr 20, 2025, 3:02 AM

by Sedro, Apr 20, 2025, 2:09 AM

by pedronis, Apr 19, 2025, 12:14 AM