pow:start
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pow:start [2025/11/18 23:27] mazur |
pow:start [2025/12/03 00:52] (current) mazur |
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| ====== Problem of the Week ====== | ====== Problem of the Week ====== | ||
| ~~NOTOC~~ | ~~NOTOC~~ | ||
| - | <box 85% round orange| Problem 7 (due Monday, December 1 )> | + | <box 85% round orange| > |
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| + | The problem of the week will return in the Spring 26 semester. We thank everyone who participated this Fall. For the winter break, we suggest reviewing all the problems from the Fall and working on the additional problems posted at the bottom of the provided solutions. | ||
| - | Consider an $m\times n$ rectangle divided into $mn$ unit squares. Let $T$ be the set of all vertices of the unit squares. At each point of $T$ we draw a short arrow (say of length $1/2$) pointing up, down, left, or right | ||
| - | with the condition that no arrow sticks outside the rectangle. Prove that regardless of how the arrows are chosen, | ||
| - | there always must exist two vertices of the same unit square at which the arrows point in opposite directions. | ||
| </box> | </box> | ||
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| ===== Previous Problems and Solutions===== | ===== Previous Problems and Solutions===== | ||
| - | * [[pow:Problem6f25|Problem 6]] Solution submitted by Gerald Marchesi and Mathew Wolak. | + | |
| + | * [[pow:Problem7f25|Problem 7]] Solved by Levi Axelrod and Matt Wolak. | ||
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| + | * [[pow:Problem6f25|Problem 6]] Solution submitted by Gerald Marchesi, Trinidad Segovia (a freshman student at Purdue University), and Mathew Wolak. | ||
| * [[pow:Problem5f25|Problem 5]] Solution submitted by Ashton Keith (Purdue University), Gerald Marchesi, and Alif Miah. | * [[pow:Problem5f25|Problem 5]] Solution submitted by Ashton Keith (Purdue University), Gerald Marchesi, and Alif Miah. | ||
pow/start.1763526427.txt · Last modified: 2025/11/18 23:27 by mazur