In comparison with several previous editions, this contest has some more difficult problems, though part of the problem set remains simple.

Among all problems, the problem setters consider problems A and G the eaiest. Problem A involves some simple matrix arithmetic. Two matrices X and Y has to be cleverly designed so that the product XⁿY would contain S as a submatrix. And there is several (possibly well-known) methods to construct a solution to problem G.

Problems B, C, F and H are somewhat harder.

In problem B, the easiest solution to implement is to enumerate how light is reflected. Since there are at most eight mirrors, the number of possibilities would not be too large. Rest of the work is devoted to check for each possibility whether reflections do not occur off the mirrors.

Problem C is solved by putting the given vectors into a matrix and performing row reductions. But since it does not accept division (otherwise equivalence cannot be preserved), reduction between two vectors has to been done in a similar manner to the Euclidean algorithm for finding greatest common divisor.

Problem F describes an impartial combinatorial game. The Sprague-Grundy theorem applies to this game. The difficulty lies in the decomposition of a position into simpler positions. It can be proved that a position with multiple heads is the sum of positions each taking exactly one distinct heads coin from the original position.

Problem H would probably deny any simple-minded search algorithms for the state space is really large. There are many approaches to construct a solution. One of them iteratively tries to fix the rightmost column and the bottommost row, thus reducing the puzzle to a smaller one. The sample test case shows that when the “three puzzle” is solvable, hence the whole puzzle is also solvable.

Problems D and E are the most difficult ones. Problem D requires to recognize the so-called complement-reducible graphs, or cographs. One characterization of cographs is that they do not contain P₄ (a path of four vertices) as induced subgraphs. There are linear time algorithms to recognize cographs.

An efficient solution to problem E can be quite complex. First, the tree has to be partitioned into a collection of paths such that the path between any two nodes share edges with only O(log n) paths in the collection. Then query can be replaced by several subqueries on paths in the collection. Segment trees should be used to support fast modifications and queries.