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Can this enumeration problem be generalized? (counting $20$-subsets of $\{1,2,3,\dots 30\}$ with no three consecutive elements)

BMO2 2017 Question 4 - Bobby's Safe

Solve: $2^{\cos^{2014}x} - 2^{\sin^{2014} x} = \cos^{2013} (2x)$

Four kissing circles

IMO 2013 Problem 6

A functional relation which is satisfied by $\cos x$ and $\sin x$

Computing the last non-zero digit of ${1027 \choose 41}$?

Prove that $(\sqrt2 − 1)^n, \forall n \in \mathbb{Z^+}$ can be represented as $\sqrt{m} − \sqrt{m−1}$ for some $m \in \mathbb{Z^+}$ (no induction).

finite polynomials satisfy $|f(x)|\le 2^x$

Is the finite sum of factorials constant modulo the summation limit?

Prove that the given sequence contains all natural numbers

Find all integer solutions to $x^2+4=y^3$. [duplicate]

Bisector proof in an olympiad level problem

If $xy+xz+yz=1+2xyz$ then $\sqrt{x}+\sqrt{y}+\sqrt{z}\geq2$.

Without calculator prove that $\log^211+\log^29<\log99$

New posts in contest-math

Frullani integral $\int_0^\infty \frac{\text{csch}(x)-\frac1x}{x} {\rm d}x$

solution to $ 7^{a}+1 =3^{b}+5^{c} $ for natural $a$,$b$ and $c$

How are inequalities from IMO built?

Every $3\times 3$ square has even number of painted cells

A nice and hard colouring problem

Can this enumeration problem be generalized? (counting $20$-subsets of $\{1,2,3,\dots 30\}$ with no three consecutive elements)

BMO2 2017 Question 4 - Bobby's Safe

Solve: $2^{\cos^{2014}x} - 2^{\sin^{2014} x} = \cos^{2013} (2x)$

Four kissing circles

IMO 2013 Problem 6

A functional relation which is satisfied by $\cos x$ and $\sin x$

Computing the last non-zero digit of ${1027 \choose 41}$?

Prove that $(\sqrt2 − 1)^n, \forall n \in \mathbb{Z^+}$ can be represented as $\sqrt{m} − \sqrt{m−1}$ for some $m \in \mathbb{Z^+}$ (no induction).

finite polynomials satisfy $|f(x)|\le 2^x$

Is the finite sum of factorials constant modulo the summation limit?

Prove that the given sequence contains all natural numbers

Find all integer solutions to $x^2+4=y^3$. [duplicate]

Bisector proof in an olympiad level problem

If $xy+xz+yz=1+2xyz$ then $\sqrt{x}+\sqrt{y}+\sqrt{z}\geq2$.

Without calculator prove that $\log^211+\log^29<\log99$