The Queens’ Islands: A Puzzle of Royal Domains
In a distant archipelago, four powerful queens ruled over four beautiful islands. Known by their signature colors—blue, red, green, and pink—these monarchs presided over territories of equal size but vastly different character. Each island boasted unique flora and fauna, creating a diverse tapestry of natural wonders across the archipelago. Despite the beauty surrounding them, the queens were consumed by ambition, each plotting to seize control of all four islands for herself. Tensions mounted as armies mobilized and alliances shifted. The archipelago teetered on the brink of a devastating war that would have destroyed much of what made these islands special.
Fortunately, the queens’ daughters—princesses who had grown up together during times of peace—recognized the impending disaster. Unlike their power-hungry mothers, the princesses valued harmony and diversity. They gathered secretly at a neutral meeting point and devised an ingenious compromise that might satisfy their mothers’ territorial ambitions while preserving peace. Their solution was elegant in its simplicity yet complex in its execution: each island would be divided into a grid of 20 equal plots, with each queen receiving exactly five plots on each island. This arrangement would allow all queens to experience the unique treasures each island had to offer while preventing any single monarch from gaining dominance.
The princesses understood that simply dividing the islands randomly would lead to disputes, so they established crucial rules for this partition. Each queen’s territory on any given island had to form a single, connected region—no isolated plots or fragmented domains would be allowed. This would simplify governance and reduce opportunities for conflict. Additionally, the four royal territories on each island needed to meet at precisely one corner point, creating a symbolic junction where the queens’ influences would converge. This arrangement would serve as a reminder of their interconnectedness and mutual dependence. Perhaps most importantly, to prevent outside powers from exploiting divisions between the queens, the exact borders of these territories would remain a closely guarded secret.
Curiosity about this mysterious arrangement of royal territories consumed me. I dispatched my most trusted assistant to infiltrate the islands and learn the truth about their divisions. After weeks of dangerous reconnaissance, my assistant returned with partial maps of the arrangements. The first island’s divisions were completely revealed, showing how the queens had divided its twenty plots. For the second and third islands, my assistant managed to discover only the shapes of the territories, not which queen controlled which region. The fourth island remained the most mysterious, with my assistant gathering only a single intriguing clue: on this final island, no two royal territories shared the same shape, not even as mirror images of each other. This puzzle of royal domains now lay before me, challenging my understanding of geometry and territorial division.
The maps presented a fascinating geometric puzzle. On the first island, the blue queen’s territory formed an L-shape in the northwest, while the red queen controlled a rectangular region in the northeast. The green queen’s domain occupied the southeast in another L-configuration, while the pink queen ruled over a T-shaped territory in the southwest. All four domains indeed met at a single corner near the island’s center. The second and third islands showed only the shapes of territories without indicating which queen controlled which region. The patterns varied significantly from the first island, with some territories forming unusual zigzag patterns or asymmetrical arrangements, though always maintaining the rule that all four domains connected at one corner point.
This puzzle of royal territories represents more than just a geometric challenge—it symbolizes how compromise and clever division of resources can prevent conflict. The princesses’ solution transformed a potential war into a delicate balance of power. While each queen may have preferred complete dominion over all islands, the arrangement satisfied their desire for diversity while preventing any single monarch from gaining an advantage. As I work to complete the missing parts of these maps, I reflect on how this puzzle mirrors real-world challenges of resource allocation and territorial disputes. Perhaps there’s wisdom in the princesses’ approach that could apply beyond their fictional realm—a reminder that creative compromises and clear boundaries can transform seemingly intractable conflicts into stable, if complex, peace.
