Once upon a time, in a faraway kingdom, there lived a king who loved mathematics more than anything else in the world. He was always looking for new and interesting problems to solve, and one day he heard about a magical polytope that could grant wishes to whoever could solve its secrets.

The king gathered all of his bravest knights and set off on a journey to find the polytope. After many days of travel, they finally stumbled upon a beautiful meadow filled with strange shapes and numbers. In the center of the meadow was the polytope, shimmering in the sunlight.

The king approached the polytope and said, "I have come to solve your secrets and claim my reward." The polytope replied, "Very well, but be warned. The task is not easy. You must use all of your mathematical knowledge to find the answer."

The king, not one to be intimidated, said, "Bring it on!" and the polytope began to present him with a series of mathematical challenges.

First, the polytope asked the king to find the maximum value in a range using a radix sort. The king thought for a moment and then wrote down the solution using a prefix tree.

Next, the polytope asked the king to traverse a quadtree using a breadth-first search, and the king confidently wrote down the solution using a queue.

The polytope then presented the king with a tricky problem involving predicates and recursion. The king worked tirelessly, using his knowledge of posets, and finally found the solution.

The polytope was impressed by the king's mathematical prowess and granted him his wish. The king wished for a never-ending supply of mathematical challenges to keep him entertained for the rest of his life.

And so, the king returned home, happy and fulfilled, with a newfound love for the beauty and complexity of mathematics. From that day on, he was known as the Mathematical King, and his kingdom was filled with joy and wonder.

The end.

Reflections

1. What was the king's wish when he solved the secrets of the magic polytope?
2. What was the first challenge the king faced when he approached the magic polytope?
3. How did the king solve the problem involving predicates and recursion?
4. What was the king's new title after solving the secrets of the magic polytope?
5. Can you think of a wish you would ask for if you were in the king's place?
6. Why do you think the king loved mathematics so much?
7. Can you name some of the mathematical concepts that the king used in his journey?
8. What does the word "polytope" mean?
9. How did the kingdom change after the king's return from his journey?
10. Do you think you could solve the challenges the king faced at the magic polytope? Why or why not?