Intereting Posts

Solving an integral with substitution method
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
Provenance of Hilbert quote on table, chair, beer mug
Another integral with Catalan
Modules over commutative rings
Lambda calculus: How to define a function that simulates $\neg p\vee q$?
Formula relating Euler characteristics $\chi(A)$, $\chi(X)$, $\chi(Y)$, $\chi(Y \cup_f X)$ when $X$ and $Y$ are finite.
How to show that $X_t = \frac{1}{\left| B_t -x\right|}\mathbb{1}_{\left\{ B_t \neq x\right\}}$ (“inverse brownian”) is a martingale?
Continuity based on restricted continuity of two subsets
Let $\alpha,\beta$ be the distinct positive roots of the equation $\tan x=2x$,then find $\int_{0}^{1}\sin \alpha x \sin \beta x$dx
proving that this ideal is radical or the generator is irreducible
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
Is there a $G_\delta$ set with Positive Measure and Empty Interior?
Proof of Hasse-Minkowski over Number Field
show that if $2^n -1$ is prime than n is also prime

A regular decagon and a regular dodecagon have been tiled with rhombuses. In each case, the sides of the rhombuses are the

same length as the sides of the regular polygon.

How many rhombuses will be there in a tiling by rhombuses of a $2002$-gon?

- What are the total number of ordered permutations of a list of elements (possibly repeated)?
- Simplify a combinatorial sum
- Which is the explanation of the identity $\sum_{k=0}^n {n \choose k}k^2 = 2^{n-2}n(n+1)$?
- Number of distinct arrangements {$n_i$} $n_1<n_2<n_3<n_4<n_5$ such that $\sum n_i=20$
- $4$ letter words taken from the letters of CONCENTRATIONS
- A problem with my reasoning in a problem about combinations

$A) 2002$

$B) 500 × 1001$

$C) 1000 × 1001$

$D) 1000 × 2002$

Could someone share please share the thought process of this question? I am not able to initiate it.

- Possible Playable Chords on a Guitar
- $4$ letter words taken from the letters of CONCENTRATIONS
- How long does a sequence need to be to be guaranteed to have a monotonic subsequence length k?
- Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
- What is the probability of this exact same Champions League draw?
- “Binomiable” numbers
- What are the properties of these two functions?
- Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
- Strong equidistribution of points on the n-sphere
- Combinatorics: Number of subsets with cardinality k with 1 element.

This is not an answer but a hint.

(No alternate way to place a figure.)

Look at the labelization I have done of your figures: how many rhombii do you have with the same label ? Generalize… by thinking to a certain arithmetic progression.

- Will this procedure generate random points uniformly distributed within a given circle? Proof?
- Complex Zeros of $z^2e^z-z$
- Integration and differentiation of Fourier series
- How to compute the pade approximation?
- Remainder in polynomial division
- $n\times n$ chessboard game with coins
- question about extension ideal
- Transpose of Volterra operator
- How to determine the limit of $ f(x, y)=\frac{9xy}{x^2 + y^2}$?
- Chain rule for composition of $\mathbb C$ differentiable functions
- Pairwise Independent Random Variables that aren't Jointly Independent
- Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
- Showing a bijection between the set of ringhomomorphisms $\mathbb{Z} \to R$ and the set of $x \in R$ for which $x^2+1=0$
- Compact operators on an infinite dimensional Banach space cannot be surjective
- About 0.999… = 1