brain

We are given a single flattened sequence that was produced from several hidden integer sequences. The encoding process mixed all sequences together in “column order”: first all first elements of each sequence, then all second elements, then all third elements, and so on.

We are given two strings consisting only of two symbols, a “minus” and a “plus”. The only allowed move takes two neighboring minus signs and replaces them with a single plus sign, which shortens the string by one character.

We are given two numbers per query, and each query hides a simple structure built from three unknown positive integers $a$, $b$, and $c$. From these three values we can form three pairwise sums: $a+b$, $a+c$, and $b+c$.

The city is a sequence of unit square buildings placed along an infinite horizontal line. Each building occupies an interval of length one, starting at some integer coordinate $ai$. So building $i$ spans $[ai, ai + 1]$, and these positions are strictly increasing.

We are given an array where every element lies between 1 and x, and we consider a transformation defined by a value interval [l, r]. This transformation deletes every array element whose value falls inside that interval, while leaving all other elements in their original order.

We are given an unknown ordering of six fixed numbers: 4, 8, 15, 16, 23, and 42. Each number appears exactly once in an array of length six, but their positions are hidden.

We are given an array of distinct numbers, and we look at every possible contiguous subarray. For each subarray, we temporarily reorder its elements in increasing order, then assign weights based on position in that sorted subarray: the smallest element gets weight 1, the next…

We are given a sequence that starts from a very simple base and then evolves through a multiplicative recurrence.

We are given a timeline of events. At any moment, Hiasat’s profile has a single visible handle, and he is allowed to change this handle only at specific moments marked in the input. Between changes, the handle stays fixed.

We are given a collection of judges. Each judge contributes two values: a number $ai$, which controls how “resistant” their opinion is, and a cost parameter $ei$, which is the time cost if we decide to interact with that judge. We may choose to play with a judge at most once.

We are interacting with a hidden number $a$, which is fixed for each game and lies between 1 and $10^9$. We cannot query it directly. Instead, we can ask questions consisting of two non-negative integers $x$ and $y$, and the judge compares $x bmod a$ and $y bmod a$.

We are given a set of people positioned on a number line. Each person is either a rider or a taxi driver, and all positions are distinct and already sorted in increasing order.

A spherical planet of radius $R$ is filled with an incompressible жидкость of constant density $\rho$ in hydrostatic equilibrium under its own gravitational field.

A uniform rope of linear mass density $\lambda$ (kg/m) passes over a frictionless pulley.

The system consists of the Sun, the Moon, and an observer on Earth.

A neon lamp consists of two large parallel plate electrodes separated by a distance $d = 3 \times 10^{-3},\text{m}$.

A planet of mass $M$ and radius $R$ is surrounded by an atmosphere of height $H$.