The Rules / Instructions of Mexican Train Dominoes (mastersofgames.com)

4. Abby, Brad, Charlene, and David are playing Mexican Train with a set of Double 12 dominioes. All player's trains are out, so all open spots are available to be played on. Prove that if Abby plays a double at the one and only legal position that there must be a satisfying domino in either a player's hand or in the boneyard. 5. Extra Credit Same setup for the above Mexican Train ques- tion, except that Abby has two legal positions to play her dou- ble. Prove or disprove that there must be a satisfying domino left to be played