user14432: Each pawn, of which there are 8 white, can move 1 or 2 squares forward.
Each knight, of which there are 2 white can move forward and left or forward and right.
That gives 20.
But white can also resign, and in some tournament situations this might be sensible.
But is resignation a move?
I sometimes attend quiz nights and this is a common question, and the answer is always said to be 20. I,  however, always say it is really 21 because of the resignation option. But, is resignation actually a move?

user4418: According to the FIDE rating regulations -


Unplayed Games
5.1 Whether these occur because of forfeiture or any other reason, they are not counted. Any game where both players have made at least
  one move will be rated.


It looks like "resigns" is not a move. Games will only be rated if each side has moved at least one piece.
I believe this regulation was introduced after an incident in the last round of a big weekend tournament in England in the mid 1970's. Tony Miles was leading the competition and only needed a draw in the last round to guarantee sole first place. He met his opponent, Stewart Reuben, in the bar the night before and agreed a draw. The next day they played no moves and simply wrote on their scoresheets "draw agreed". Tony Miles won first place and Stewart Reuben shared second with several other players. They were given their prize money and everybody was happy until somebody noticed they had played no moves. Then the organizer was unhappy. The result between Miles and Reuben was cancelled and they were required to repay their prize money. Now this practice is explicitly banned.
If you look in the FIDE Laws of Chess you see that the full title of article 3 is -

Article 3: The moves of the pieces

From this you can also see that in chess moves are moves of pieces. "Resigns" is not a move of a piece and is therefore not a move.
So, the correct answer is 20. 

user7473: Your question essentially reduces to asking whether resignation is considered a move or not. To be exact, you are asking about legal moves, the topic of which is addressed in (and defined by) Article 3 of the Laws of Chess. Resignation isn't mentioned there, so it's not a move.
A heuristic argument: you are allowed to make a move and then resign immediately, i.e. if resignation was a move, you have effectively made two consecutive moves, which is not allowed.
Or more simply: since you can resign even when it's not your move, it follows that resignation is not considered a move.

14432: <p>Each pawn, of which there are 8 white, can move 1 or 2 squares forward.
Each knight, of which there are 2 white can move forward and left or forward and right.</p>

<p>That gives 20.</p>

<p>But white can also resign, and in some tournament situations this might be sensible.</p>

<p>But is resignation a move?</p>

<p>I sometimes attend quiz nights and this is a common question, and the answer is always said to be 20. I,  however, always say it is really 21 because of the resignation option. But, is resignation actually a move?</p>
 4418: <p>According to the FIDE <a href="https://www.fide.com/fide/handbook.html?id=197&amp;view=article" rel="noreferrer">rating regulations</a> -</p>

<blockquote>
  <ol start="5">
  <li><p>Unplayed Games</p>
  
  <p>5.1 Whether these occur because of forfeiture or any other reason, they are not counted. Any game where both players have made at least
  one move will be rated.</p></li>
  </ol>
</blockquote>

<p>It looks like "resigns" is not a move. Games will only be rated if each side has moved at least one piece.</p>

<p>I believe this regulation was introduced after an incident in the last round of a big weekend tournament in England in the mid 1970's. Tony Miles was leading the competition and only needed a draw in the last round to guarantee sole first place. He met his opponent, Stewart Reuben, in the bar the night before and agreed a draw. The next day they played no moves and simply wrote on their scoresheets "draw agreed". Tony Miles won first place and Stewart Reuben shared second with several other players. They were given their prize money and everybody was happy until somebody noticed they had played no moves. Then the organizer was unhappy. The result between Miles and Reuben was cancelled and they were required to repay their prize money. Now this practice is explicitly banned.</p>

<p>If you look in the <a href="https://www.fide.com/fide/handbook.html?id=171&amp;view=article" rel="noreferrer">FIDE Laws of Chess</a> you see that the full title of article 3 is -</p>

<blockquote>
  <p>Article 3: The moves of the pieces</p>
</blockquote>

<p>From this you can also see that in chess moves are moves of pieces. "Resigns" is not a move of a piece and is therefore not a move.</p>

<p>So, the correct answer is 20. </p>
 7473: <p>Your question essentially reduces to asking whether resignation is considered a move or not. To be exact, you are asking about <em>legal</em> moves, the topic of which is addressed in (and defined by) Article 3 of the <a href="https://www.fide.com/fide/handbook.html?id=171&amp;view=article" rel="noreferrer">Laws of Chess</a>. Resignation isn't mentioned there, so it's not a move.</p>

<p>A heuristic argument: you are allowed to make a move and then resign immediately, i.e. if resignation was a move, you have effectively made two consecutive moves, which is not allowed.</p>

<p>Or more simply: since you can resign even when it's not your move, it follows that resignation is not considered a move.</p>
