Trigonometry - worm thread related word problem

A sum involving a binomial Determine if $x^3+y^3+z^3+t^3 = 10^{2021}$ has a solution Prove that $\frac{a^2}{a^2+bc}+\frac{b^2}{b^2+ac}+\frac{c^2}{c^2+ab}<2$ Prove there are infinitely many squares ending in the digits $54321$ Comparison test for $\sum_{n=1}^{\infty} \frac{\sqrt{n^5 + n^3 - n}}{2n^3 + 3n^2 + 1}$ A conditional probability problem where the next day depends on the last 3 days Numerically evaluating $\iiint_{C} \frac{ {\rm d}x \, {\rm d}y \, {\rm d}z}{x^2 +y^2 + z^2}$ Finding probability distribution from given moments Pattern for all the binary chains divisible by 5 How Many Uniquely Enumerated $4\times4$ Sudoku Grids Exist? What does Cohen independence theorem say? What's the intuition behind the Co-Area formula?