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Dan
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I like math questions that:

  • can be expressed concisely
  • contain few or no numbers
  • are challenging
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All Questions Answers
Score Newest
question
39
Conjecture: If circular coins of any sizes are in a convex polygonal frame, with each coin touching exactly one edge, then all the coins can move
Jan 11
question
31
On average, how many uniformly random real numbers $u$ are needed for their sum to exceed $1$, if $u_1$ is in $(0,1)$ and $u_k$ is in $(0,eu_{k-1})$?
Feb 23
question
25
Does there exist a continuous function $f(x)$ such that $f(0)=0$ and $0<\lim_{n\to\infty}\prod_{k=1}^n f(k/n)<\infty$?
Nov 16, 2022
question
16
Are there general principles that allow us to easily determine whether coins in simple arrangements in a frame can move?
Jan 12
question
15
Conjecture: If equal size circular coins are in a convex polygonal frame, with each coin touching exactly one edge, then all the coins can move
Jan 12
question
13
Regular $n$-gon with diagonals: bounds on area of largest cell?
Dec 17, 2022
question
11
Can a billiard rack be a square, for every number of balls?
Jan 6
question
8
You have $n$ rectangles of area $1$ and variable height. Pack as many as possible in a semicircle of area $n$. How many leftovers will there be?
May 31
question
5
Given $n$, how to find integers $a_0,...,a_n$ so that $\sum_{k=0}^n a_k x^k$ has $n$ distinct real roots, and $\max{(|a_0|,...,|a_n|)}$ is minimized?
Apr 5
question
4
Can a convex frame hold all circles of radius $1/n$ immobile?
Jan 18
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40
Regular polygon of radius $1$ with diagonals: mysterious ring of radius $1/e$?
36
Crazy fact(?) about circles drawn on base of triangle between cevians: they always fit, no matter what their order?
34
What is the mean value of $|\sin x +\sin (\pi x)|$?
32
Coin Flip Probability Independent or Not?
31
‘Lies to children’ in mathematics and statistics education

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