A Domino Chain of Sums 
       
|1 3|2 0|

Place the dominos 1-3, and 2-0 together in a line. By taking all the pips in unbroken conjunction I can get all the numbers from 1 to 6 inclusive. Thus 1, 2, and 3 can be taken alone; then 1 and 3 make 4; 3 and 2 make 5; and the entire set makes 6. It would not have been allowed to take the 1 and the 2 to make 3. The numbers would not have been in conjunction.
  1. Take any two dominos from a double-6 set and place them in a chain so that you can make the pips in this way sum to any number from 1 to N, where N is as large as possible. As above, the dominos need not be placed 1 against 1, 2 against 2, and so on, as in play.
  2. Same question for three dominos.
  3. Same question for four dominos.

Source: Henry Ernest Dudeny, 536 Curious Problems & Puzzles, #481.

Solution
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