Learn Through Visuals

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Rotate Image — The Mural Turn

Dungeon 18, Boss 1. A museum's square mosaic mural must make a quarter turn clockwise, but the tiles are mortared to a frame that cannot move, and no second frame exists. All you can do is swap tiles in place. Mirror the mural across its diagonal, then flip each row, and two reflections quietly add up to one rotation.

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Spiral Matrix — The Spiral Plow

Dungeon 18, Boss 2. A farmer plows a rectangular field in a spiral, never crossing a furrow he's already cut, and you have to write down the order the soil turns. Four boundary fences that shrink inward do the whole job, but skip one mid-loop check and a single-row field gets plowed twice.

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Set Matrix Zeroes — The Condemned Rows

Dungeon 18, Boss 3. A building inspector walks a grid of storage units where one structural failure condemns an entire corridor and an entire stack. No notebook allowed, so every marking has to go on the units themselves. The matrix's own first row and column become the clipboard, and the order you erase them decides everything.

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Happy Number — The Numerologist's Loop

Dungeon 18, Boss 4. A carnival numerologist runs your lucky number through a ritual: square each digit, add them up, repeat. Some numbers ascend to 1 and are declared happy. Others circle the same values forever. Spot the trap without waiting forever, using a cycle detector you already own from the linked list dungeon.

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Plus One — The Odometer Tick

Dungeon 18, Boss 5. An old mechanical odometer needs one more mile ticked onto it. Most miles just bump the last wheel, but a wheel at 9 rolls to 0 and nudges its neighbor, and a full row of 9s needs a brand new wheel bolted on the front. Walk the digits backward, return early, and meet carry propagation in base 10.

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Pow(x, n) — The Paper Fold

Dungeon 18, Boss 6. A paper craftsman has to build a stack that doubles in thickness a billion times, and gluing one layer at a time would outlive him. Then he folds the strip once and everything changes: one fold doubles the whole stack. Computing x to a huge power works the same way — square what you have instead of multiplying one at a time, and two billion steps collapse into thirty-one.