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Solve for x, y, and z in the following equation: x29 + y30 + z31 = 366.

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Using algebra or matrix mechanics, solve for x, y, and z. Where x, y, and z are positive integers, and where zero is not an integer or part of an integer.

29x+30y+31z=366. What is the value of x , y, and z? In order to answer the question correctly, you must provide 2 sets of numbers which will satisfy the equation.

Hint: A simple leap year calendar will solve for one set.

Hint #2: Algebra will also solve for another/both sets of numbers. However, a simple 2D matrix (columns and rows) will allow for a quick and easy visualization of the 2 sets of numbers.

Conclusion: Matrices and Feynman type diagrams are often more powerful tools than algebra. Learn to use both, for they are very effective problem solving devices in situations where algebra is too tedious or complicated. And for those that are mathematically challenged and think in terms of pictures rather than numbers, Matrices and Diagrams may be the best solution.

posted Sep 4, 2016 by George Davros

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1 Answer

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Using hint 1: A simple leap year calendar will solve for one set.
A leap year have 1(x) no.of month-29days(x), 4(y) no.of month-30 days, 7(z) no.of month - 31 days, so solution x=1,y=4,z=7

answer Sep 5, 2016 by Lekshmanan Perumal Murugan

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