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The same wizard from this problem decides to cast a more complicated transmutation spell, this time with five spell components: copper, tin, silver, lead, and gold. The spell matrix is …

A robot starts on a dot of a grid, makes $20$ moves of one unit with each move in a randomly selected direction (up, down, left, or right), and then …

You are given a 20-sided regular polygon. Find the number of pairs of diagonals that intersect either in the interior of the polygon or the exterior of the polygon. …

You are in an open field with two coins and you alternate flipping the coins and taking steps by the following rules:

If both coins are heads, then you take …

Two robots play a game of tic-tac-toe. They choose their moves randomly. Let $E$ denote the expected number of moves it would take for the robots to finish a game. …

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