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====== Problem of the Week ====== | ====== Problem of the Week ====== | ||
~~NOTOC~~ | ~~NOTOC~~ | ||
- | <box 85% round orange|Problem 2 (due Monday, February 17) > | + | <box 85% round orange| > |
- | Let $d(n)$ be the smallest number such that among any $d(n)$ points inside a regular $n$-gon with side of length 1 | + | The problem of the week will return in the Fall 2024 semester. We thank everyone who participated this Spring. For the Summer, we suggest reviewing problems from past semesters and working on the additional problems posted at the bottom of the provided solutions. |
- | there are two points whose distance from each other is at most 1. Prove that | + | |
- | + | ||
- | (a) $d(n)=n$ for $4\leq n\leq 6$. | + | |
- | + | ||
- | (b) $\displaystyle \lim_{n\to \infty} \frac{d(n)}{n}=\infty $. | + | |
</box> | </box> | ||
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===== Previous Problems and Solutions===== | ===== Previous Problems and Solutions===== | ||
+ | * [[pow:Problem7s24|Problem 7]] Solved by Sasha Aksenchuk. | ||
+ | |||
+ | * [[pow:Problem6s24|Problem 6]] Solved by Sasha Aksenchuk. | ||
+ | |||
+ | * [[pow:Problem5s24|Problem 5]] We did not receive any solutions. | ||
+ | |||
+ | * [[pow:Problem4s24|Problem 4]] A solution submitted by Beatrice Antoinette. | ||
+ | |||
+ | * [[pow:Problem3s24|Problem 3]] Solved by Mithun Padinhare Veettil. | ||
- | * [[pow:Problem2s24|Problem 2]] Solutions | + | * [[pow:Problem2s24|Problem 2]] A solution submitted by Sasha Aksenchuk. |
* [[pow:Problem1s24|Problem 1]] Solutions submitted by Sasha Aksenchuk and Maximo Rodriguez. | * [[pow:Problem1s24|Problem 1]] Solutions submitted by Sasha Aksenchuk and Maximo Rodriguez. |