What fraction is shaded?

Prove or disprove that in an 8-element subsets of $\{1,2…,30\}$ there must exist two $4$-element subsets that sum to the same number.

Secretary problem - Riemann integral

Ring of integers of $\mathbb{Q}(\sqrt[3]{6})$

Let $A$ be a real $2×2$ matrix such that $A^6=I$. The total number of possibilities for the characteristic polynomial of $A$ is:

Is it true that $A_n$ contains all the elements of odd order?

Show that $x(t)<0$ for all $t>0$

Whats wrong with this model theoretic proof of the twin primes conjecture?

$\text{det}(\text{abs}({\bf d - d}^T))$ being zero implies two or more elements equal in $\bf d$?

Show that there are infinitely many natural numbers such that $a^2+b^2=c^2+3 .$

Looking for introductory text on algebraic topology, not satisfied with Hatcher.

Determine, by its action on an orthonormal basis, whether a linear operator can be continuous

Could you generate any positive number given only a few specific operators and operands?

Related