user1512: I just read that Alexander Alekhine simultaneously played 26 blindfold games.
Are blindfold players allowed to look at the list of moves? Can they re-create the position in their mind from the list of moves, or do they have to memorize the position on each table?

user1105: What I'm going to say is too long for a comment so I guess I have to answer. This is funny because I'm the one who marked your question as favorite, just in case someone answers it, I wanted to know the answer, and here I am the one who's answering it!
Do you know what were the rules of these competitions ?
No but I'll keep searching, maybe I can provide a better answer later on. If you only want to read my answer to your question scroll down, it's the last part.

But I guess, that Alexander Alekhine did not look at anything when playing. I will tell you why I think he didn't look, I will tell you how I think he was able to do it. Lets look at other things that our mind can do, and we'll talk about chess in the end.

Did you know that many Muslims are required to memorize each word of the Quran? They actually do competitions sometimes to see who can answer faster, many none Arabic Muslims do that even little kids, imagine how hard it would be for a small kid to memorize the entire Quran, in Arabic, a language that he doesn't even understand.
How many songs can you memorize? at least 1000 but you don't know it yet. How many songs can singers memorize? How many music compositions can musicians play without looking at the notes?
What Is the Memory Capacity of the Human Brain?

You can do this, untrained, normal person, what can a professional do?

To fully understand what the brain is capable of you should take a look at:

Stan Lee's Superhumans with The Human Calculator Scott Flansburg
The Musical Genius - Derek Paravicini
The Rubik's cube Brazilian solver

Lets talk about the second example in particular, that guy is autistic and blind, so the brain adapted to the situation and his memory becomes so good that he could play any music he ever heard any time, perfectly.
Those are more exceptional people but still untrained.

Lets talk about chess now, all the chess players, at least all the GMs are trained professionally from a very young age to play chess.
What would a trained chess kid be able to do? What would a 13 year old kid do nowadays? play xbox, listen to Justin Bieber, watch cartoon network...
What would a 13 years old chess player do? Well Fischer at the age of 13 did the most amazing checkmate ever against Donald Byrne, I think no supercomputer will be able to do what Fisher did, it was called the game of the century.
I talked about how good the brain could become at certain things like memorization, but I still haven't answer your initial question!

You should know that Alexander Alekhine isn't the current record holder.

Timur Gareev performs 33-board blindfold simul in Saint Louis
History of Blindfold chess

I quote from the second article:

George Koltanowski set the world's blindfold record on 1937 by playing
  34 chess games simultaneously while blindfolded, winning 24 games and
  losing 10, over a period of 13 hours. The record was included in the
  Guinness Book of Records and is generally accepted as the world record
  to this day.

And most importantly

Miguel Najdorf increased this record to 45 opponents in 1947, with the
  result of 39 wins, four draws and two losses.However, he had access to
  the scoresheets, and there were multiple opponents per
  board.Koltanowski claimed that he could have managed 100 games under
  those conditions.

So you can see why i don't think Alekhine had access to the scoresheets, otherwise they wouldn't have accepted his record, which is exactly what happened with Najdorf. Besides the players who challenged Alekhine, would feel it's unfair to challenge a great GM, with access to scoresheets, he would beat them all so easily.
Now how do I personally think he did it?

He challenged amateurs, 800 - 1400 Elo max
He played one or two openings against all of them so he doesn't have to remember many openings
He played aggressive opening that he knows so well so he can finish the games so fast and not having to worry about middle game calculations

And finally from Wikipedia I guess the answer you wanted to know

Occasionally, grandmasters have given blindfold simultaneous displays.
  In such displays, the exhibitor does not look at any of the boards,
  but retains all the moves of the games in his/her head. The opponents
  utilize boards and pieces in the standard fashion, but their moves are
  communicated verbally to the exhibitor by an arbiter or intermediary.

Note
I don't think that GMs rely on their visual memory so much, but rather they do something like meditation, where they create their own games inside their heads and visualize it.

user1606: They memorize the position on each table; In this kind of event, they simply don't have the time to spend to much time on each position. Also trying to re-create the position like this is not practical when you play blindfold chess
If you want to know (almost) everything on blindfold play, check out this great book on 
http://www.blindfoldchess.net/
Cheers!

1512: <p>I just read that Alexander Alekhine simultaneously played 26 blindfold games.</p>

<p>Are blindfold players allowed to look at the list of moves? Can they re-create the position in their mind from the list of moves, or do they have to memorize the position on each table?</p>
 1105: <p>What I'm going to say is too long for a comment so I guess I have to answer. This is funny because I'm the one who marked your question as favorite, just in case someone answers it, I wanted to know the answer, and here I am the one who's answering it!</p>

<p><strong>Do you know what were the rules of these competitions ?</strong></p>

<p>No but I'll keep searching, maybe I can provide a better answer later on. If you only want to read my answer to your question scroll down, it's the last part.</p>

<hr>

<p>But I guess, that Alexander Alekhine did not look at anything when playing. I will tell you why I think he didn't look, I will tell you how I think he was able to do it. Lets look at other things that our mind can do, and we'll talk about chess in the end.</p>

<ul>
<li>Did you know that many Muslims are required to memorize each word of the Quran? They actually do competitions sometimes to see who can answer faster, many none Arabic Muslims do that even little kids, imagine how hard it would be for a small kid to memorize the entire Quran, in Arabic, a language that he doesn't even understand.</li>
<li>How many songs can you memorize? at least 1000 but you don't know it yet. How many songs can singers memorize? How many music compositions can musicians play without looking at the notes?</li>
<li><a href="http://www.scientificamerican.com/article.cfm?id=what-is-the-memory-capacity" rel="nofollow">What Is the Memory Capacity of the Human Brain?</a></li>
</ul>

<p>You can do this, untrained, normal person, what can a professional do?</p>

<hr>

<p>To fully understand what the brain is capable of you should take a look at:</p>

<ul>
<li><a href="https://www.youtube.com/watch?v=fQot4v5yHKE" rel="nofollow">Stan Lee's Superhumans with The Human Calculator Scott Flansburg</a></li>
<li><a href="https://www.youtube.com/watch?v=fibZudrZUto" rel="nofollow">The Musical Genius - Derek Paravicini</a></li>
<li><a href="https://www.youtube.com/watch?v=GklYRMbJwUA" rel="nofollow">The Rubik's cube Brazilian solver</a></li>
</ul>

<p>Lets talk about the second example in particular, that guy is autistic and blind, so the brain adapted to the situation and his memory becomes so good that he could play any music he ever heard any time, perfectly.</p>

<p>Those are more exceptional people but still untrained.</p>

<hr>

<p>Lets talk about chess now, all the chess players, at least all the GMs are trained professionally from a very young age to play chess.</p>

<p>What would a trained chess kid be able to do? What would a 13 year old kid do nowadays? play xbox, listen to Justin Bieber, watch cartoon network...</p>

<p>What would a 13 years old chess player do? Well Fischer at the age of 13 did the most amazing checkmate ever against Donald Byrne, I think no supercomputer will be able to do what Fisher did, it was called <a href="http://www.youtube.com/watch?v=M624T3PTggU" rel="nofollow">the game of the century</a>.</p>

<p>I talked about how good the brain could become at certain things like memorization, but I still haven't answer your initial question!</p>

<hr>

<p>You should know that Alexander Alekhine isn't the current record holder.</p>

<ul>
<li><a href="http://www.chessvibes.com/reports/timur-gareev-performs-33-board-blindfold-simul-in-saint-louis" rel="nofollow">Timur Gareev performs 33-board blindfold simul in Saint Louis</a></li>
<li><a href="http://www.chess.com/article/view/history-of-blindfold-chess" rel="nofollow">History of Blindfold chess</a></li>
</ul>

<p>I quote from the second article:</p>

<blockquote>
  <p>George Koltanowski set the world's blindfold record on 1937 by playing
  34 chess games simultaneously while blindfolded, winning 24 games and
  losing 10, over a period of 13 hours. The record was included in the
  Guinness Book of Records and is generally accepted as the world record
  to this day.</p>
</blockquote>

<p>And most importantly</p>

<blockquote>
  <p>Miguel Najdorf increased this record to 45 opponents in 1947, with the
  result of 39 wins, four draws and two losses.However, he had access to
  the scoresheets, and there were multiple opponents per
  board.Koltanowski claimed that he could have managed 100 games under
  those conditions.</p>
</blockquote>

<p>So you can see why i don't think Alekhine had access to the scoresheets, otherwise they wouldn't have accepted his record, which is exactly what happened with Najdorf. Besides the players who challenged Alekhine, would feel it's unfair to challenge a great GM, with access to scoresheets, he would beat them all so easily.</p>

<p>Now how do I personally think he did it?</p>

<ul>
<li>He challenged amateurs, 800 - 1400 Elo max</li>
<li>He played one or two openings against all of them so he doesn't have to remember many openings</li>
<li>He played aggressive opening that he knows so well so he can finish the games so fast and not having to worry about middle game calculations</li>
</ul>

<p>And finally from <a href="http://en.wikipedia.org/wiki/Simultaneous_exhibition#Procedure" rel="nofollow">Wikipedia</a> I guess the answer you wanted to know</p>

<blockquote>
  <p>Occasionally, grandmasters have given blindfold simultaneous displays.
  In such displays, the exhibitor does not look at any of the boards,
  but retains all the moves of the games in his/her head. The opponents
  utilize boards and pieces in the standard fashion, but their moves are
  communicated verbally to the exhibitor by an arbiter or intermediary.</p>
</blockquote>

<p><strong>Note</strong></p>

<p>I don't think that GMs rely on their visual memory so much, but rather they do something like meditation, where they create their own games inside their heads and visualize it.</p>
 1606: <p>They memorize the position on each table; In this kind of event, they simply don't have the time to spend to much time on each position. Also trying to re-create the position like this is not practical when you play blindfold chess</p>

<p>If you want to know (almost) everything on blindfold play, check out this great book on 
<a href="http://www.blindfoldchess.net/" rel="nofollow">http://www.blindfoldchess.net/</a></p>

<p>Cheers!</p>
