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We are given a graph of post offices connected by bidirectional routes. A message starts at some office, travels along a simple path to another office, and at every intermediate office the message’s “mark” is flipped.

We are given a sequence of n days. On each day i there are two exchange rates: one for dollars and one for Brazilian reals, both measured in Egyptian pounds.

We are given a straight railway line where every point can be treated as an integer coordinate on a number line. Each resident has a home position and a work position on this line, and they start walking toward work at time zero with speed 1 unit per second.

We are given an undirected weighted graph representing cities connected by roads. Initially, the graph is connected. Each road has a strength value. A road is considered “critical” if removing it disconnects the graph. In graph terms, this is exactly a bridge.

We are building a number of grams of food that Thiago will offer. Each valid offering must be composed of baskets of fixed size A, so the total amount must be a multiple of A.

We are given two sets of entities: historians and paintings. Each historian can be assigned to at most one painting, and each painting can be assigned to at most one historian, so any valid solution is a matching in a bipartite graph.

We are given a collection of words, each paired with a positive value. A valid “spell” is a sequence of words where every next word must extend the previous one by exactly one or more characters, meaning the previous word is a proper prefix of the next.

We are given several independent strings, each representing a name made of lowercase English letters. The transformation rule defines how a new version of the string is constructed: every character is inspected together with its immediate neighbors, and the character is…

We start with a row of spheres labeled from 1 to N in increasing order. Two agents repeatedly shrink this row by removing every second remaining element, but they sweep in opposite directions.

We are given a collection of $n$ distinct primes $a1, a2, dots, an$. From these primes we form a single huge product $P = prod ai$. Each item in the store is defined in an unusual way: the price of item $i$ is the product of all primes except $ai$.

We are maintaining a sequence of numbers arranged in a line, where each position represents a fig tree and the value at that position is the number of figs on that tree.

There are three independent taxi services, each running an infinite sequence of shared tuk-tuks between a city center and a hotel. Each service has its own travel time and capacity.

We are given a collection of time intervals, each representing the construction period of a building. A chosen day corresponds to sending the army to inspect all buildings that are under construction on that day.

I can’t reliably write a correct editorial for this without the actual problem statement. “Codeforces 103937I - Moldy Sandwich” isn’t something I can reconstruct from metadata alone, and guessing would almost certainly produce a wrong solution, wrong algorithm, and…

A monotone Boolean function $f(x1,dots,x5)$ is uniquely represented by its set of minimal true points, an antichain $A subseteq 2^{[5]}$, and conversely every antichain determines such a function by upward closure.

Let $f$ be a Boolean function represented by an ordered reduced BDD, and let $x_j$ be the variable being eliminated.

The problem statement for Codeforces 103937H - Competing Clubs is not included in your message (the “Problem Statement / Input / Output” sections are empty).

The problem statement is missing, so I can’t accurately reconstruct or explain the solution for “Codeforces 103937G - Larry Longsleeves”.

I can’t produce a correct editorial for this problem as-is because the actual problem statement (the definitions of “diverse debaters”, input format, and required output) is missing.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103937F - Bat-shoe Toss is not included in your message.

I don’t have the actual statement of Codeforces 103937D “Hardcore Haircuts” in your prompt, so I can’t reliably reconstruct the problem or produce a correct editorial.

At the moment, there is no description of what the input represents, what operations are allowed, or what must be computed as output.

I don’t have the actual statement of Codeforces 103937A - Jeopardy! in your prompt, and without it I can’t reliably reconstruct the intended task, constraints, or solution path.

Algorithm C in this section evaluates a BDD bottom-up by assigning to each node $v$ a value depending only on its LO and HI successors, with sink nodes providing the base cases and each internal node combining results from its children.

I can’t produce a correct editorial yet because the actual problem statement for Codeforces 103938I - Moldy Sandwich isn’t included in your message.

The problem statement for Codeforces 103938J - Quantum Chaos is missing from your prompt, so I don’t have any information about what the task actually asks (input format, required output, or the underlying model).

Algorithm C in this section evaluates a BDD bottom-up by assigning to each node $v$ a value depending only on its LO and HI successors, with sink nodes providing the base cases and each internal node combining results from its children.

I can’t produce a correct editorial yet because the problem statement is missing. Right now the only information provided is the title “Competing Clubs”, but there is no description of the rules, input format, or required output.

I can’t safely write a correct editorial yet because the full problem statement for “103938G - Larry Longsleeves” is not reliably available from your prompt, and the title alone is not enough to reconstruct the exact task without risking inventing details.

The problem statement is not included in your prompt, so I don’t have the actual rules, input format, or required computation for Codeforces 103938F - Bat-shoe Toss.

I can’t reliably write a correct editorial for this problem yet because the statement for “Codeforces 103938D - Hardcore Haircuts” is missing from your prompt.

I’m missing the actual problem statement for Codeforces 103938C - Robot Inspection, so I can’t reliably reconstruct the task or derive a correct algorithm without guessing.

Let a multiset ${a_1,\dots,a_n}$ be given, and assume Algorithm L of Section 7.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only know the title “Limited Increasing Sequences”, but there is no definition of: what the input represents, what constraints apply, or what needs to be computed.

Let $f(x1,dots,xn)$ be a Boolean function with truth table $tau$ and BDD $T(f)$. Recall from Section 7.1.4 that a function is sweet when every subtable corresponding to a prefix assignment is a bead, equivalently every node in its ordered decision structure corresponds to a…

The problem statement is missing (the Input/Output and actual description are empty), so there’s no way to reconstruct the task reliably from what you provided.

I’m missing the actual problem statement for Codeforces 103940J - Joining the KAK, so I can’t reliably reconstruct the intended model or derive a correct solution yet.

The problem statement section is empty, so I don’t have enough information to reconstruct what “How Many Laughs” is asking or what the input/output represent.

I can write the full Codeforces-style editorial, but I’m missing the actual problem statement for 103940I - Inversion Counting.

The problem statement is missing from your prompt, so there is no way to reconstruct the task, constraints, or required algorithm reliably.

I’m missing the actual problem statement for Codeforces 103940F - Famous Paintings, so I can’t safely reconstruct the solution or write a correct editorial.

The problem statement is missing from your prompt, so there isn’t enough information to derive the solution, constraints, or even the core task for “Express Warehouse Migration”.

The problem statement is missing from your prompt, so there’s no way to reconstruct the task, constraints, or required output.

I can’t write a correct editorial for this yet because the actual problem statement is missing. Right now I only have the title “Correcting School Enrollment Errors”, but no definition of the input, output, or constraints.

I don’t have the actual statement for Codeforces 103940A - Advanced Player Setup, so I can’t reliably reconstruct the problem or produce a correct editorial without guessing.

We are given a tree with n nodes, and each node carries a distinct label from 0 to n − 1, so the labels form a permutation.

We are given a multiset of short strings, each up to length 5000 in total across all inputs. From these strings, we care about which longer strings “qualify” certain fragments. A fragment is a partition of a string t into consecutive pieces.

We are given a function on the set of integers from 1 to n. Each number points to exactly one number in the same range, so the function can be seen as a directed graph where every node has exactly one outgoing edge. We are also given many queries.

We are given a three dimensional grid representing a building. Every point in this grid is a room identified by coordinates $(x, y, z)$. Movement inside this building is not done by walking, but by using special cyclic elevators.

We are given several binary strings, all of equal length. Think of them as a matrix with n rows and m columns, where each entry is either 0 or 1. Each row is a string, and each column is a bit position shared across all strings. We then perform a sequence of operations.

The problem gives a grid of size 4 by m. The top row contains exactly one entry point at column x, and water starts flowing downward from that cell. The bottom row contains exactly one exit point at column y, and it can only accept water flowing downward into it.

We are working with finite sets of non-negative integers. Given a set $A$, we define the sumset $A + A$ as all values that can be formed by adding any two elements from $A$, with repetition allowed in the choice but duplicates removed in the result.

We are given a single long string made of lowercase English letters. From this string, we are allowed to delete characters and keep the remaining ones in order, forming a subsequence.

A Boolean function is sweet when every subtable arising from any prefix assignment is a bead. A truth table is a bead exactly when it is not of the form $alphaalpha$, so every subfunction must have distinct LO and HI subtables at every node of its ordered decision structure.

We are given a convex polygon that rotates rigidly around a fixed point, which is guaranteed to lie inside the polygon or on its boundary. Along with this, we are given two parallel lines that form an infinite strip.

We are given a string over the alphabet A, B, C, D that changes over time. Two operations are supported: we can cyclically increment every character in a range, and we can ask how many different “exam papers” could produce a given substring while using exactly k questions.

We are given a circular string made only of four characters, each mapped to a small integer weight. The string is arranged in a ring, so after the last character we wrap back to the first.

A truth table of order $n$ is a binary string of length $2^n$. A bead is a truth table $beta$ that is not of the form $alphaalpha$. A Boolean function is sweet if every subtable obtained by fixing any prefix of variables is a bead.

We are given a grid of size $R times C$ where each cell contains either a known integer or a missing value represented by a question mark.

We are given the coordinates of all vertices of a convex polyhedron in three-dimensional space. We are allowed to rotate this solid arbitrarily in 3D, then “shine a light” from a fixed direction and look at the orthogonal projection of the polyhedron onto a plane.

A truth table of order $n$ is a binary string of length $2^n$. A bead is a truth table $beta$ that is not of the form $alphaalpha$. A Boolean function is sweet if every subtable obtained by fixing any prefix of variables is a bead.

Each test case gives a collection of identical vertical blocks, where every block is a cuboid with one fixed dimension equal to 1 and two other dimensions $ai$ and $bi$.

We are simulating a constrained random assignment process for 32 football teams. The teams are already divided into four fixed tiers, each tier containing exactly eight teams.

We are given 14 distinct playing cards. From these, we must discard exactly one card and then split the remaining 13 cards into three poker hands: a 3-card front hand, a 5-card middle hand, and a 5-card back hand.

Let $x = (x_1,\dots,x_n)_2$ and let the successor sequence in exercise 91 be $x,\, x\oplus 1,\, x\oplus 2,\, \dots,$ where $x\oplus k$ is binary addition mod $2^n$.

We are building a periodic tiling of an $R times C$ rectangle, and then repeating it infinitely in both directions. So the entire plane is determined by a finite matrix of size $R times C$, where each cell is assigned one of $K$ colors.

We are given a line of ants placed at integer positions from 1 to N. Ant i starts exactly at position i and has weight i. At time zero each ant independently chooses a direction, left or right, with equal probability. All ants then move at the same constant speed.

A truth table of order $n$ is a binary string of length $2^n$. A bead is a truth table $beta$ that is not of the form $alphaalpha$. A Boolean function is sweet if every subtable obtained by fixing any prefix of variables is a bead.

We start with a single banknote of value $A$, and we want to end up with the ability to pay exactly $B$, where $A B$. The only tool available is a vending machine: we spend some amount of money on goods, and the machine gives back change.

We are given a cyclic sequence of phases, each phase adding some value to our current amount of money. The twist is that money is never allowed to go below zero, if an operation would make it negative, it is clamped back to zero instead.

We start with a collection of boxes, each box containing some number of balls. One operation modifies this configuration in a very specific way.

Let $f(x1,dots,xn)$ be a Boolean function with truth table $tau$ of length $2^n$. A truth table is called a bead if it is not of the form $alphaalpha$.

I can’t write a correct editorial yet because the actual problem statement for Codeforces 103960M - Hopscotch Marathon is missing from your prompt.

The problem statement is missing, so I can’t reliably reconstruct what “Codeforces 103960N - Numbers on both Sides” is asking.

I don’t have the actual problem statement for “Codeforces 103960K - Kalel, the Jumping Frog” in your message, so I can’t safely reconstruct the solution or write a correct editorial.

I don’t have the actual problem statement for Codeforces 103960J - Playing 23 in your message, so I can’t safely reconstruct the logic or write a correct editorial without risking inventing details. Please paste the full problem statement (or even a screenshot/text dump).

The system is reading a single byte transmitted as eight separate signals. Each position is supposed to be a binary digit, so normally every slot should contain either 0 or 1.

We are given a simplified blackjack-style game involving two players, João and Maria. Each player starts with two cards, and then a sequence of common cards is revealed one by one.

The editorial can’t be written yet because the actual problem statement is missing. Right now we only know the title “Geometry of Triangles”, but none of the required details are provided: what is given in the input, what needs to be computed, and what constraints define…

I can’t reliably write a correct editorial for this yet because the actual problem statement for Codeforces 103960H - Helping the Transit isn’t included in your prompt. Right now I don’t know: what the input represents, what needs to be computed, or even the constraints.

I don’t have the actual statement of Codeforces 103960D - Displacing Particles in your prompt, so I can’t reliably reconstruct the problem or produce a correct editorial.

I don’t have the actual problem statement for Codeforces 103960E - Eliminating Balloons, so I can’t safely reconstruct the solution or write a correct editorial yet.

We are given a sequence of straight laser cuts performed on a sheet. The laser starts at a given point and then moves through a sequence of endpoints, where each segment represents one cut.

The problem statement is missing, so there isn’t enough information to write a correct editorial. Right now we don’t know what “Finding Maximal Non-Trivial Monotones” actually defines in terms of input, output, or operations, so any attempt to derive an algorithm would…

I can’t reliably write a correct editorial for “Codeforces 103960B - Fun with Stones” without the actual problem statement. The ID alone isn’t enough, and guessing would almost certainly produce a wrong solution and misleading explanation.

Let $f, g$ be Boolean functions on $n$ variables, and let the operator $f \downarrow g$ be defined by the ordering $x, x \oplus 1, x \oplus 2, \ldots$ on $n$-bit vectors, where $x \oplus k$ denotes bi...

We are given a partially filled 9 by 9 Sudoku grid. Each cell either already contains a digit from 1 to 9 or is empty.

We are given a set of 2n rectangular objects, each described by two numbers, height and width. The goal is not to directly assign them to two groups arbitrarily, but to count how many distinct ways there exist to choose two thresholds H and W such that everything with height…

We are given a sequence of leaf pile sizes, but these piles are positioned on a long line of positions numbered from 1 to c.

We are given a circular keyboard containing $n$ keys arranged in a fixed cyclic order. Each key holds a lowercase Latin letter, and multiple positions may share the same letter. A pointer starts on any key we choose, and we want to generate a target string $s$.

We are given $n$ stacks, which the statement calls rockets, plus one additional empty stack. Each of the $n$ types appears exactly twice across all stacks, and every stack initially contains exactly two elements, one on top of the other.

We are maintaining a dynamic array of integers, initially given, and we must support three types of operations over subarrays. The first operation asks for a weighted sum over a segment, where each element contributes its value XOR its index.

We are simulating a single train car that starts fully occupied by ordinary passengers. Later, privileged passengers arrive one by one and try to take seats as soon as possible, but seats can only become available when ordinary passengers decide to stand up.

We are given a binary grid consisting of white and red cells. The task is to determine whether we can reproduce exactly the red cells using a sequence of stamping operations with two fixed brush shapes. Each operation selects a cell and applies one of two patterns.

We are given a collection of songs, each song having a base enjoyment value. We build a playlist of length k by repeatedly choosing which song to play next.

We are given a rectangular grid of letters. The grid can be modified, but only in a very specific way: we may reorder entire rows arbitrarily and we may reorder entire columns arbitrarily.

We are given a sequence of integers. Think of them as daily “changes” to some running value that starts at zero. As we go from left to right, we maintain a running sum. Each element either increases or decreases this running sum.

Let Eq.

The problem statement is missing from your message, so I don’t have enough information to reconstruct the task or derive a correct solution.

We are given a sequence of positions arranged in a line, where each position carries a certain weight. Then we are given a collection of independent queries. Each query describes a process that starts from a given index and repeatedly jumps forward by a fixed step size.