Intereting Posts

Quadrature formula on triangle
If $\sum_{n=1}^{\infty} a_{n}^{3}$ converges does $\sum_{n=1}^{\infty} \frac{a_{n}}{n}$ converge?
Can we permute the coefficients of a polynomial so that it has NO real roots?
Idempotence of the interior of the closure
Why are Euclid axioms of geometry considered 'not sound'?
Integral of Hermite polynomial multiplied by $\exp(-x^2/2)$
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
Find a positive integer $n$ such that $ϕ(n) = ϕ(n + 1) = ϕ(n + 2)$
Linear Transformations finding matrix in respect to a basis and coordinate change matrix.
$\mathbb{C}\otimes_\mathbb{C} \mathbb{C} \cong \mathbb{R}\otimes _\mathbb{R} \mathbb{C}$
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
Rolling $2$ dice: NOT using $36$ as the base?
Probability of picking a specific value from a countably infinite set
What is known about Collatz like 3n + k?
Is it possible to 'split' coin flipping 3 ways?

So in my discrete math class, we all know that if the drawer has 2 different colored socks, you need to pull out 3 socks to ensure a pair.

However, I am puzzled after there are more different colored socks and more pairs of socks.

For example, if there are 3 different colored socks in the drawer and I need to draw out 50 pairs, at least how many socks do I need to draw out to ensure that I have 50 pairs of sock?

- Draw a finite state machine which will accept the regular expression $(a^2)^* + (b^3)^*$
- Card probability problem
- Can a collection of points be recovered from its multiset of distances?
- Proof By Induction - Factorials
- Relation between bernoulli number recursions
- $x_1+x_2+\cdots+x_n\leq M$: Cardinality of Solution Set is $C(M+n, n)$

How about if there are M different colored socks in the drawer and I need to draw out N pairs, at least how many socks do I need to draw out to ensure that I have N pairs of sock?

Are there any general formulas for these types of problem? Or are there any rules for this type of question?

- Induction proof (bitstring length)
- How many bins do random numbers fill?
- How do you derive the continuous analog of the discrete sequence $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, …$?
- Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
- Notation Question: What does $\vdash$ mean in logic?
- What are some mathematically interesting computations involving matrices?
- Coin flipping probability game ; 7 flips vs 8 flips
- Infiniteness of non-twin primes.
- pigeonhole principle and division
- Prove with induction that $11$ divides $10^{2n}-1$ for all natural numbers.

The maximum is clearly achieved when there is an odd quantity of socks of each color(A proof by contradiction is immediate). If you have $2c_1+1,2c_2+1,\dots ,2c_M+1$ socks of each of the $M$ colors then you have $c_1+c_2\dots +c_m$ pairs and $2(c_1+c_2+\dots c_M)+m$ socks. Then the maximum socks you can have without $N$ pairs is $2(N-1)+m$

- Is zero irrational?
- Why do bell curves appear everywhere?
- A method of finding the eigenvector that I don't fully understand
- Finding $\int^1_0 \frac{\log(1+x)}{x}dx$ without series expansion
- How a group represents the passage of time?
- Why is $0^0$ also known as indeterminate?
- Find generators of a group in GAP
- The motivation of weak topology in the definition of CW complex
- Is the set theory (ZF) a structure?
- If $\sqrt{a} + \sqrt{b}$ is rational then prove $\sqrt{a}$ and $\sqrt{b}$ are rational
- on the boundary of analytic functions
- Books for starting with analysis
- $\frac{1}{{1 + {\left\| A \right\|} }} \le {\left\| {{{(I – A)}^{ – 1}}} \right\|}$
- Puzzle : There are two lengths of rope …
- Show that $\sqrt{n^2+1}-n$ converges to 0