Papers on arXiv solving the same problem at the same time I am little bit curious about the following examples 

at least two papers appeared on arxiv at the same day solving one
  and the same problem.

Have you ever seen such a coincidence? If yes, can you provide the links to that papers? 


*

*of course the papers maybe solving one and the same problem in a slightly different generalities, for example, one solved a certain case of the problem, and the other one solved the problem completely.

*the authors should be different, for example, it is not allowed that  both papers have one and the same person as an author/co-author.
 A: This happened in 2013 in the context of finding $\epsilon$-approximate solutions to the maximum $s-t$ flow problem in near-linear-time (taking day to mean any 24 hour period).
The two references are https://arxiv.org/abs/1304.2338 (Jonathan A. Kelner, Yin Tat Lee, Lorenzo Orecchia, Aaron Sidford) and https://arxiv.org/abs/1304.2077 (Jonah Sherman).
As usual, the timing was not a coincidence.
A: I presume the OP is looking for examples from mathematics. Here is one:
Hadrien De March, Nizar Touzi: Irreducible convex paving for decomposition of multi-dimensional martingale transport plans (submitted February 27, 2017, at 14.23 hours)   
Jan Obłój, Pietro Siorpaes: Structure of martingale transports in finite dimensions (submitted February 27, 2017, at 18.52 hours)
The second paper explains:

Finally we note that we have hoped to make this paper publicly
  available only after having proved Conjecture 1.3. However we have
  been recently made aware of a parallel and independent work of De
  March and Touzi who study the same problem and obtain similar
  results using different techniques. Consequently, we have agreed to
  simultaneously make our works publicly available.

A: Here's an example from equivariant homotopy theory. Blumberg and Hill,
studying multiplicative structures on equivariant spectra, defined a functor from the (homotopy) category of
$N_\infty$-operads to the category of indexing systems, and conjectured that it's an equivalence of categories.
Three teams of researchers proved this conjecture at around the same time!
Rubin posted his proof in May 2017, followed soon after by Bonventre and
Pereira and Gutiérrez and White, who posted
theirs on the same day in July. The latter two groups were aware of each other, and deliberately synchronized.
In this case, having three proofs is good: the proofs are different, and each proof has different advantages and
disadvantages. Moreover, the papers do more than just resolve the conjecture; each has different additional
material.
A: Yesterday I also circulated this question to my colleagues and one more example was brought to my attention. 
https://arxiv.org/abs/1905.11968
https://arxiv.org/abs/1905.11877
(both of them appeared on arXiv on 28 May 2019)
They solve the following problem: one receives a convex body  $K_{0}$ in $\mathbb{R}^{n}$ and chooses a point $x_{0} \in K_{0}$, then one receives another convex body $K_{1}$, and chooses a point $x_{1} \in K_{1}$ etc. The goal is after $N$ steps to make the total distance between these points $\sum_{i=1}^{N}\| x_{j}-x_{j-1}\|$  minimal. They both find an algorithm such that  $\frac{\sum_{i=1}^{N}\| x_{j}-x_{j-1}\|}{\sum_{i=1}^{N}\| \tilde{x}_{j}-\tilde{x}_{j-1}\|} \leq O(\sqrt{n \ln N})$, where $\sum_{i=1}^{N}\| \tilde{x}_{j}-\tilde{x}_{j-1}\|$ is the smallest distance one could get if one would in advance knew positions and shapes of all convex bodies $\{K_{j}\}_{j=0}^{N}$. 
UPDATE: looks like they also are synchronized. Right before the section 2 the author of the first paper writes

After this work was completed, we were informed that C.J. Argue, Anupam Gupta, Guru
  Guruganesh, and Ziye Tang jointly obtained similar results for this problem. Both preprints are
  being posted to the ArXiv simultaneously.

A: I was involved in one such pair:


*

*Van den Berg, Garner, Types are weak $\omega$-groupoids, https://arxiv.org/abs/0812.0298

*Lumsdaine, Weak $\omega$-categories from intensional type theory, https://arxiv.org/abs/0812.0409
(different calendar dates in UTC, but within 12 hours of each other, and the same day in the time zone where the latter was submitted)
These have the same main result: constructing a weak $\omega$-category structure on the terms of a type and its iterated identity types in Martin-Löf type theory.
As in several other answers, the timing is not a coincidence: we’d become aware of the overlapping result while we were both writing up the papers, so we acknowledged each other’s work and co-ordinated the posting.
A: Brian Greene, in his book "The Elegant Universe" on p. 280 (I'm looking at the original 1999 edition as far as I can tell), writes:
"In January 1993, Witten and the three of us released our papers simultaneously to the electronic Internet archive through which physics papers are immediately made available worldwide. The two papers described, from our widely different perspectives, the first examples of topology-changing transitions - the technical name for the space-tearing processes we had found. The long-standing question about whether the fabric of space can tear had been settled quantitatively by string theory."
The papers in question are hep-th/9301042 (Witten, Phases of $N=2$ Theories In Two Dimensions) and hep-th/9301043 (Aspinwall–Greene–Morrison, Multiple Mirror Manifolds and Topology Change in String Theory), both submitted on January 12, 1993.
