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36 votes

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Show that the sequence $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,\cdots$ isn't periodic

answered Aug 30, 2013 at 17:07

35 votes

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Can a row of five equilateral triangles tile a big equilateral triangle?

answered Apr 17, 2017 at 1:35

25 votes

Proving $\sum_{k=0}^n(-1)^k\binom nk=0$

answered Dec 27, 2011 at 19:54

23 votes

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What is the significance of the power of $3$ in the sequence of primes given by $\lfloor A^{3^n}\rfloor ?$

answered Aug 23, 2013 at 0:51

15 votes

Longest known sequence of identical consecutive Collatz sequence lengths?

answered Aug 19, 2013 at 0:28

15 votes

What are the theorems in mathematics which can be proved using completely different ideas?

answered Jan 18, 2015 at 13:10

15 votes

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Find all polynomials that fix $\mathbb Q$ and the irrationals

answered Dec 20, 2012 at 3:19

13 votes

Unusual mathematical terms

answered Jan 13, 2015 at 22:05

12 votes

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Finding the GCD of three numbers?

answered Dec 23, 2011 at 18:37

10 votes

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Simple proof that stationary birth-death chains are reversible

answered Feb 10, 2012 at 0:01

9 votes

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Partitions of $\{1,\dots,n\}$ with no consecutive integers in each block is counted by $B(n-1)$?

answered Jan 29, 2012 at 22:08

9 votes

What is the problem in this solution to the Two Child Problem?

answered Dec 24, 2011 at 23:36

9 votes

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If a finite set of rational numbers sums to one, does one of the rationals have a denominator equal to the LCM of all the denominators?

answered Dec 25, 2011 at 21:48

8 votes

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Remember trig identities like $\cos(\pi/3) = 1/2$

answered Feb 3, 2012 at 23:51

8 votes

Graph on the cover of Bollobás's "Combinatorics"

answered Dec 20, 2012 at 19:05

7 votes

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Inequality $a^2+b^2+c^2 \leq a^2b+b^2c+c^2a+1. $

answered Jan 5, 2013 at 0:39

7 votes

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Regular hexagon on a colored sphere

answered Dec 23, 2011 at 23:39

6 votes

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Controlling the coefficients of the factors of a polynomial with integer coefficients

answered Dec 20, 2012 at 21:41

5 votes

probability unordered sample

answered Dec 28, 2011 at 18:04

4 votes

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Number of ways to assign numbers $1,2,\ldots, n$ to $x$ red balls and $y$ blue balls, $x+y = n$, in a set of $X$ red and $Y$ blue.

answered Dec 30, 2011 at 22:28

4 votes

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$\ell_p$ space for $p<1$

answered Feb 5, 2012 at 17:34

4 votes

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Contest problem on domain and range of square root function

answered Feb 2, 2012 at 1:29

4 votes

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Congruence question

answered Feb 3, 2012 at 2:09

3 votes

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Finding the least significant digit of a large exponential.

answered Feb 3, 2012 at 2:56

3 votes

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How do I write this simple proof (Dedekind cuts) in Mathese?

answered Feb 3, 2012 at 22:51

3 votes

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A couple of questions using Ramsey Theorem

answered Feb 5, 2012 at 18:41

3 votes

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Using the Catalan numbers

answered Jan 2, 2012 at 15:25

3 votes

Singing Bird Problem

answered Feb 13, 2012 at 21:37

3 votes

Counting (and enumerating) pairs

answered Feb 21, 2012 at 1:02

3 votes

Covering spaces - why are they useful?

answered Dec 31, 2011 at 0:05

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54 Answers

Show that the sequence $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,\cdots$ isn't periodic

Can a row of five equilateral triangles tile a big equilateral triangle?

Proving $\sum_{k=0}^n(-1)^k\binom nk=0$

What is the significance of the power of $3$ in the sequence of primes given by $\lfloor A^{3^n}\rfloor ?$

Longest known sequence of identical consecutive Collatz sequence lengths?

What are the theorems in mathematics which can be proved using completely different ideas?

Find all polynomials that fix $\mathbb Q$ and the irrationals

Unusual mathematical terms

Finding the GCD of three numbers?

Simple proof that stationary birth-death chains are reversible

Partitions of $\{1,\dots,n\}$ with no consecutive integers in each block is counted by $B(n-1)$?

What is the problem in this solution to the Two Child Problem?

If a finite set of rational numbers sums to one, does one of the rationals have a denominator equal to the LCM of all the denominators?

Remember trig identities like $\cos(\pi/3) = 1/2$

Graph on the cover of Bollobás's "Combinatorics"

Inequality $a^2+b^2+c^2 \leq a^2b+b^2c+c^2a+1. $

Regular hexagon on a colored sphere

Controlling the coefficients of the factors of a polynomial with integer coefficients

probability unordered sample

Number of ways to assign numbers $1,2,\ldots, n$ to $x$ red balls and $y$ blue balls, $x+y = n$, in a set of $X$ red and $Y$ blue.

$\ell_p$ space for $p<1$

Contest problem on domain and range of square root function

Congruence question

Finding the least significant digit of a large exponential.

How do I write this simple proof (Dedekind cuts) in Mathese?

A couple of questions using Ramsey Theorem

Using the Catalan numbers

Singing Bird Problem

Counting (and enumerating) pairs

Covering spaces - why are they useful?