## Search found 11 matches

Thu May 17, 2018 2:34 pm
Forum: Primary Level
Topic: Not too unkind
Replies: 2
Views: 3301

### Re: Not too unkind

Solution to a modified G6. Mathmash round 15 P8
Thu May 17, 2018 2:24 pm
Forum: Primary Level
Topic: Not too unkind
Replies: 2
Views: 3301

### Not too unkind

. Note that \$EF\| ST\$ implies that \$M\$ lies on the median from \$A\$ of \$\triangle {AST}\$. As the reflection of \$M\$ in \$ST\$ lies on the\$\odot{AST}\$, we conclude that \$AK\$ is a symmedian in \$\triangle{AST}\$, and hence in \$\triangle{AEF}\$as well. Since \$K\$ lies on the perpendicular bisector of \$EF\$, we ...
Tue Feb 20, 2018 11:32 am
Forum: Combinatorics
Topic: triangle in a square has area less than 1/2
Replies: 5
Views: 6206

### Re: triangle in a square has area less than 1/2

Take a square of length \$n\$ and choose \$(n+1)^2\$ points inside the square. Prove that, you can choose some \$3\$ points so that the triangle made by them has an area at most \$\dfrac12\$. It is a nice problem. Sketch of solution: Take the convex hull of points H. Apparently,the hull has area at most n^...
Mon Feb 19, 2018 1:00 pm
Forum: Combinatorics
Topic: triangle in a square has area less than 1/2
Replies: 5
Views: 6206

### Re: triangle in a square has area less than 1/2

Silly me.Couldn't latex for shortage of time :"(
Mon Feb 19, 2018 12:59 pm
Forum: Combinatorics
Topic: triangle in a square has area less than 1/2
Replies: 5
Views: 6206

### Re: triangle in a square has area less than 1/2

Take a square of length \$n\$ and choose \$(n+1)^2\$ points inside the square. Prove that, you can choose some \$3\$ points so that the triangle made by them has an area at most \$\dfrac12\$. It is a nice problem. Sketch of solution: Take the convex hull of points . Denote it by H.Apparently,the hull has a...
Mon Feb 19, 2018 12:45 pm
Forum: Combinatorics
Topic: বিয়ে
Replies: 6
Views: 8746

### Re: বিয়ে

Sat Feb 17, 2018 1:41 am
SN.Pushpita wrote:
Thu Feb 15, 2018 1:38 pm
Are you proud of your knowledge regarding Hall's Marriage Lemma?:p
Yes, yes I am proud of my knowledge of marriage procedures.
Dude, it isn't mathoscope
Thu Feb 15, 2018 2:24 pm
Forum: Combinatorics
Topic: n-series
Replies: 1
Views: 4441

### Re: n-series

First observe that for any sequence, if the first 3 terms are a,b and c respectively,then either b<a <c or c <a <b will hold. Now repeating the condition given in the question and fixing the number of terms u can get the order of each sequence.So FOR each subset of cardinality >=3 of {1,2,3,....n} u...
Thu Feb 15, 2018 1:38 pm
Forum: Combinatorics
Topic: বিয়ে
Replies: 6
Views: 8746

### Re: বিয়ে

Are you proud of your knowledge regarding Hall's Marriage Lemma?:p
Wed Feb 14, 2018 1:20 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 29278

### Re: Combi Marathon

First one has holes but the second one is correct.
Wed Feb 14, 2018 1:06 pm
Forum: Combinatorics
Topic: Combi Marathon
Replies: 48
Views: 29278

### Re: Combi Marathon

Problem 20 A pentagon with all sides equal is given. Prove that the circles having those sides as diameters can't cover the the entire region of that pentagon. Sketch of solution: This claim is true for convex pentagon.For any convex pentagon,the summation of internal angles is 540 and 540-3×60=2×1...