USCF Ruling - Resignation confusion after reaching results sheet At a tournament I was participating in last weekend, there was an interesting situation that happened and the TD did not know how to handle the situation.

White said something along the lines of "I think you should resign," but thought White had said "I think I'll resign". Black put his hand out and White shook Black's hand. Neither player said anything after this, but packed away the set and only when they went to write their result did they realize that they misunderstood each other.

What should happen here? Is the game drawn because they shook hands?
The correct decision here is to send the players back to finish their game.  There's a very good rule of thumb that TD's use in situations like this - if the two players don't agree on the result of the game (there's no "meeting of the minds" between the players), they should go back to the board and continue the game.

It's up to the TD to set the clock times as reasonably as possible.  For example, if it's an hour into the round of a G/60 tournament and a spectator saw that white was up 10 minutes on the clock, it might be appropriate to set the clocks to 25 minutes for black and 35 minutes for white.  Nothing is going to be perfect, but so long as both players have at least a few minutes, allowing the players to determine the outcome on the board is going to be far better than the TD adjudicating the game.

As a rule, the absolute last resort for TD's should be to adjudicate the result of a game.  Everything possible should be done to allow the result to be determined by the players via play.  

Finally, the TD does have some discretion in cases like this.  If the next round is about to start, and there's no time to allow the players to finish the game, the TD can have the players adjourn their game and pair the next round using his or her best guess as to the result.  One trick with adjournments is that the TD can pair the players as if one of them has won the game and the other has drawn the game.  This has the benefit of making sure that neither player gets unduly easy pairings in the next round before the result of the game is actually determined.