Problem 20 · 2009 Math Kangaroo
Hard
Algebra & Patterns
magic-squaresubstitution
The sum of the numbers in each row, column and diagonal in the “magic square” on the right is always constant. Only two numbers are visible. Which number is missing in field a?
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Answer: D — 55
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Hint 1 of 2
Use that every line, column and both diagonals share the same total S.
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Hint 2 of 2
Combine a few of those equal-sum lines so the unknown cell pops out on its own.
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Approach: add and subtract equal-sum lines to isolate the corner
- Writing each row, column and diagonal as equal to S gives a linear system in the cells.
- Combining the equations forces the corner cell a to a single value regardless of the others.
- That value is 55.
Mark:
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