Can you arrange fifteen of the pieces round a track like this so that all the touching domino pieces add to $6$ and the ends join up?
You will have six pieces left over.
Using the same twenty-one pieces, can you now make all the joins add to $7$? Which six pieces will you have to leave out?
Can you now make all the joins add to $5$ using the twenty-one pieces? Which six pieces will you have to leave out now?
Now can you make all the joins add to make an even number? What about all the joins adding to make an odd number?
You may find our Dominoes Environment useful for working on this problem.Printable NRICH Roadshow resources: Instructions and Domino Track.