E N I G M A

SQUARED DEAL

by M.J.P. Wolf

The United Square Republics have been together so long that the boundaries between the individual republics have vanished from most maps. As the USR’s cartographer, you have been commissioned to reconstruct a map of the 21 individual republics that make up the USR, in order to settle the dispute as to which republic the capital, Quadra, resides in. The USR covers an area of land, square in shape and 112 miles to a side, with Quadra in the exact center of the square. Each of the 21 republics is also square

in shape, and each have whole numbers of miles to a side; but no two republics are the same size. Though it may hard to believe at first, the 21 square republics completely tile the entire area of the USR. From the ten pieces of information gathered below, determine the size and position of each of the republics within the USR, and which republic Quadra lies in.

A. The largest republic is exactly 625 times the land area of the smallest one, and the combined area of the six smallest republics is equal to exactly one tenth the land area of the largest republic.

B. The land area of the second largest republic is 49 times the area of the third smallest republic, and 36 times the area of the fourth smallest republic.

C. Voth has exactly as much land area as the combined areas of Dorra, Froll, Gom, and Bolta.

D. Merm is exactly one-fourth the land area of Curro, one-ninth the land area of Phydra, and over 20 times the land area of Zevo.

E. Bolta is larger than Nurin, which is 1000 square miles larger than Gom. There are also four republics which are each larger than Gom by less than 150 square miles.

F. Alto is four times the land area of Telka, and Telka has as much land area as Dorra and Slome combined.

G. Hort is 16 times the land area of Elga, and Elga is smaller than Froll but is larger than Zevo.

H. Jarp lies in one of the corners of the USR, and shares a border with Wintz, and they both border Elga.

I. Koid borders Okell to the east, and neither borders Rudra. Rudra does share borders with Lenif, Phydra, and Nurin.

J. Hort borders Dorra to the south and Okell borders Dorra to the north

The solution will be revealed in next issue.

---EXTROPY #15 (7:2) 2nd-3rd Quarter 1995

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