Solving 100 Bushels Using Matrix Factorization
John Mount discusses a solution to the "100 Bushels of Corn" puzzle using matrix factorization, highlighting its educational value in teaching Diophantine equations and linear algebra concepts.
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The article discusses a solution to the "100 Bushels of Corn" puzzle, which involves distributing 100 bushels among 100 people, with men receiving 3 bushels, women 2 bushels, and children 0.5 bushels each. The author, John Mount, highlights the puzzle as a practical example for demonstrating tools used in solving Diophantine equations. He presents a matrix factorization approach to arrive at the solution, emphasizing its educational value in understanding linear algebra concepts. The article serves as an announcement for a more detailed write-up that will be available for further reading.
- The "100 Bushels of Corn" puzzle involves distributing bushels among men, women, and children.
- John Mount provides a matrix factorization solution to the puzzle.
- The puzzle serves as a practical example for teaching Diophantine equations.
- The article aims to keep the solution editable while ensuring reliable LaTeX rendering.
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5 commentsHere's a very simple alternative:
for m in range(0,100):
for w in range(0,100):
for c in range (0,100):
if m + w + c == 100 and 3*m+2*w+.5\*c==100:
print(m,w,c)Edit: related follow up: any chance this technique is a good fit for enumeration of [Magic Squares][0] of a given order?
Pretty smart parrot.
The word problem directly translates to this system of diophantine equations:
(i) { x + y + z = 100
(ii) { 6x + 4y + z = 200
(ii) <=> 6x + 4y - x - y + 100 = 200 <=> 5x + 3y = 100
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