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USSR Algebra Problem

Algebra Problem - 1980 Leningrad HS Olympiad

This is algebra Problem 7 from the 1980 Leningrad High School Olympiad, "Olympiad Corner", Crux Mathematicorum, Volume 9, Number 10, page 302. It was found in a document (missing the title page strangely enough) that is a compilation of papers presented at a weekend gathering in 1993 of mathematicians, magicians, fans, and puzzle community members as a tribute to Martin Gardner. Martin Gardner was among other things, a writer for Scientific American magazine from 1957 - 1982. The forward to the paper was written by Elwyn Berlekamp and Tom Rodgers.

The problem was taken from a section named "Puzzles from Around the World" by Richard I. Hess. It is number M6 (Medium Hard) in his set of problems. The graphic below, when clicked will enlarge to show the solution I came up with and how I got there. Thankfully, Mr. Hess provided a final answer for this problem, and the solution illustrated here agrees with that answer.

Mathematics > USSR Algebra Problem
USSR Algebra Problem This is algebra Problem 7 from the 1980 Leningrad High School Olympiad, "Olympiad Corner", Crux Mathematicorum, Volume 9, Number 10, page 302. It was found in a document (missing the title page strangely enough) that is a compilation of papers presented at a weekend gathering in 1993 of mathematicians, magicians, fans, and puzzle community members as a tribute to Martin Gardner. Martin Gardner was among other things, a writer for Scientific American magazine from 1957 - 1982. The forward to the paper was written by Elwyn Berlekamp and Tom Rodgers. The problem was taken from a section named "Puzzles from Around the World" by Richard I. Hess. It is number M6 (Medium Hard) in his set of problems. The graphic below, when clicked will enlarge to show the solution I came up with and how I got there. Thankfully, Mr. Hess provided a final answer for this problem, and the solution illustrated here agrees with that answer.