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Given $n$ balls. Among them, $n-1$ have the same weight, and one ball is heavier than the others. Determine the minimum number of weighings on a two-pan balance (without weights) required to find the heavy ball.

A store offers an assortment of toys of various types. For each type, the number of toys and the price of one toy are known. Determine the total number of toys with a price less than $50$ hryvnias.

A number is called massive if it can be written in the form $a^n$, that is, $a$ raised to the power of $n$.

For the celebration, the Professor bought balloons of three colors: blue, red, and yellow. In total, he bought $n$ balloons. The number of yellow and blue balloons is $a$, and the number of red and blue balloons is $b$.

Solve the quadratic equation $a\cdot x^2+b\cdot x+c=0(a\ne 0)$.

You are going to toast some slices of bread for an upcoming party. You have a frying pan that can hold at most $k$ toasts at the same time. Toasting one side of a toast takes $2$ minutes.

An array of $n$ integers is given. Find the number of maximum elements in the array.

The project "Average Weight of a School Student" was undertaken by Mamed and Samed.

Even in ancient times, the Egyptians knew that a triangle with sides $3$, $4$, and $5$ is a right triangle, with its right angle being the largest one. Determine whether other triangles also have this property.