Differences

This shows you the differences between two versions of the page.

--- pow:start [2024/02/07 01:58]
mazur
+++ pow:start [2024/04/23 00:06] (current)
mazur
@@ Line 2: / Line 2: @@
 ====== Problem of the Week ======
 ~~NOTOC~~
-<box 85% round orange|Problem 1 (due Monday, February 17) >
+<box 85% round orange|Problem 7 (due Monday, May 6) >
-Let $d(n)$ be the smallest number such that among any $d(n)$ points inside a regular $n$-gon with side of length 1
+Prove that for every $n\geq 1$ the number
-there are two points whose distance from each other is at most 1. Prove that
+\[ \frac{(1^2+2^2+\ldots + n^2)!}{(1!)^2\cdot(2!)^3\cdot(3!)^4\cdot\ldots \cdot(n!)^{n+1}}\]
+is an integer.
-(a) $d(n)=n$ for $n\leq 6$.
-(b) $\displaystyle \lim_{n\to \infty} \frac{d(n)}{n}=0 $.
 </box>
@@ Line 25: / Line 22: @@
 ===== Previous Problems and Solutions=====
+    * [[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]] A solution submitted by Sasha Aksenchuk.
-    * [[pow:Problem1s24|Problem 1]] Solutions submitted by
+    * [[pow:Problem1s24|Problem 1]] Solutions submitted by Sasha Aksenchuk and Maximo Rodriguez.
     * [[pow:Fall 2023]]