The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

   

The Billionaire's Inheritance

Having just relieved yourself in the guest bathroom, you and the nameless billionaire have a conversation about his nameless billionaire brother. "He was a very wonderful fellow," the billionaire explains, "and I was honored to have him as my brother, but he died recently. He left 169 square miles of land in his will. I inherited eight squares miles of that land, but since you've been so helpful to me, and since you're so smart, I'll let you have that land, if you can solve this problem."

He hands you this paper:

"My brother had divided the land into 32 parts. Each part was shaped like a rectangle or a square, with the length and height both being an exact number of miles. He had 32 houses on those 169 square miles of land, too, and he made sure that each partition of the land had exactly one house -- no more, no less. The houses are represented by numbers, which themselves indicate how many square miles of land are in that house's section. If you can show me how the land was divided up, you can have my share of the land. My portion of the land is the one on the east side of the grid which has 8 square miles."

Can you get yourself eight square miles of land?


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