pow:start
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pow:start [2026/02/23 22:37] mazur |
pow:start [2026/03/25 15:53] (current) mazur |
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| ====== Problem of the Week ====== | ====== Problem of the Week ====== | ||
| ~~NOTOC~~ | ~~NOTOC~~ | ||
| - | <box 85% round orange| Problem 2 (due Monday, February 23 ) > | + | <box 85% round orange| Problem 4 (due Monday, March 30 ) > |
| - | + | ||
| - | In a class with $n>2$ students the teacher wants to assign to each student some topics to work on in such a way that any two students have a unique common topic assigned, each topic is given to more than one student | + | |
| - | but no topic is assigned to all the students. Show that the teacher has to use at least $n$ topics. | + | |
| + | Let $n>0$ be an odd integer. Prove that there exists a set $S=\{A_1, \ldots, A_{2n}\}$ of $2n$ distinct points in the plane which are not collinear and such that if $i+j\neq 2n+1$ then the line $A_iA_j$ contains a third point from $S$. | ||
| </box> | </box> | ||
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| ===== Previous Problems and Solutions===== | ===== Previous Problems and Solutions===== | ||
| - | * [[pow:Problem2s26|Problem 2]] | + | * [[pow:Problem3s26|Problem 3]] No solutions were submitted. |
| + | |||
| + | * [[pow:Problem2s26|Problem 2]] Solved by Prof. Emmett Wyman. | ||
| * [[pow:Problem1s26|Problem 1]] No solutions were submitted. | * [[pow:Problem1s26|Problem 1]] No solutions were submitted. | ||
pow/start.1771904225.txt · Last modified: 2026/02/23 22:37 by mazur