Question

IMO/1981 - Combinatorics

score 255 · Answer 1 · 2026-05-07 07:14:07

255

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IMO/1981 - Combinatorics

Published on 07 May 2026 - 7:14

score 52 · Answer 2 · 2026-05-07 13:11:07

52

Views

Divisibility of binomial coefficient

Published on 07 May 2026 - 13:11

score 161 · Answer 3 · 2026-05-10 14:51:51

161

Views

Closed form for square of binomial CDF

Published on 10 May 2026 - 14:51

score 173 · Answer 4 · 2026-05-10 15:02:31

173

Views

Sum identity over the reciprocal of central binomial coefficients using their partial fraction decompositions.

Published on 10 May 2026 - 15:02

score 152 · Answer 5 · 2026-05-10 16:37:52

152

Views

How to prove that if $n$ is prime then ${{n}\choose{i}} = 0 \mod{n}$?

Published on 10 May 2026 - 16:37

score 181 · Answer 6 · 2026-05-06 13:38:59

181

Views

$\sum\limits_{k=0}^{\frac{n}{2}} 2k\binom{n}{2k}=n\cdot2^{n-2}$

Published on 06 May 2026 - 13:38

score 285 · Answer 7 · 2026-05-10 17:18:01

285

Views

How many rational numbers are in the opening of this binomial: $(\sqrt3+\sqrt[3]2)^{100}$

Published on 10 May 2026 - 17:18

score 319 · Answer 8 · 2026-05-10 15:47:48

319

Views

If $n$ is a multiple of $8$, then the number of sets of size divisible by $4$ is $2^{n-2} + 2^{(n-2)/2}$

Published on 10 May 2026 - 15:47

score 264 · Answer 9 · 2026-05-10 16:05:41

264

Views

Expected value of obtained dice faces by rolling a n-faced dice repeatedly

Published on 10 May 2026 - 16:05

score 849 · Answer 10 · 2026-05-10 15:46:58

849

Views

Determine the coefficient of $x^6$ in $(1 - x)^{15}$

Published on 10 May 2026 - 15:46

score 158 · Answer 11 · 2026-05-05 18:52:03

158

Views

A rational function with hidden symmetry and alternating poles and zeros.

Published on 05 May 2026 - 18:52

score 908 · Answer 12 · 2026-05-10 15:26:10

908

Views

Use a generating function to find the number of ways to distribute $r$ jelly beans among $8$ children if each child gets at least one jelly bean.

Published on 10 May 2026 - 15:26

score 359 · Answer 13 · 2026-05-10 15:44:10

359

Views

Binomial coefficient: Search for multiples of 13

Published on 10 May 2026 - 15:44

score 1.4k · Answer 14 · 2026-05-06 13:44:55

1.4k

Views

Inverse of the $n$-by-$n$ matrix $(a_{jk})$ where $a_{jk} = \binom{j-1}{k-1}$

Published on 06 May 2026 - 13:44

score 77 · Answer 15 · 2026-05-10 17:15:37

77

Views

Show that you can choose a subset of these binomial coefficients whose gcd is $1$

Published on 10 May 2026 - 17:15

List Question

IMO/1981 - Combinatorics

Divisibility of binomial coefficient

Closed form for square of binomial CDF

Sum identity over the reciprocal of central binomial coefficients using their partial fraction decompositions.

How to prove that if $n$ is prime then ${{n}\choose{i}} = 0 \mod{n}$?

$\sum\limits_{k=0}^{\frac{n}{2}} 2k\binom{n}{2k}=n\cdot2^{n-2}$

How many rational numbers are in the opening of this binomial: $(\sqrt3+\sqrt[3]2)^{100}$

If $n$ is a multiple of $8$, then the number of sets of size divisible by $4$ is $2^{n-2} + 2^{(n-2)/2}$

Expected value of obtained dice faces by rolling a n-faced dice repeatedly

Determine the coefficient of $x^6$ in $(1 - x)^{15}$

A rational function with hidden symmetry and alternating poles and zeros.

Use a generating function to find the number of ways to distribute $r$ jelly beans among $8$ children if each child gets at least one jelly bean.

Binomial coefficient: Search for multiples of 13

Inverse of the $n$-by-$n$ matrix $(a_{jk})$ where $a_{jk} = \binom{j-1}{k-1}$

Show that you can choose a subset of these binomial coefficients whose gcd is $1$

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