# Place 28 dominoes in a loop

A standard set of double-six dominoes has 28 tiles with 2 numbers on each side from 0 to 6. Tiles can be placed next to each other if the numbers at each end match. Can you place all the 28 tiles such that they form a loop? Note that the end number must also match the front number to complete the loop.

Note that

the numbers, $$0-6$$, are elements of the finite field $$\mathbb{F}_7$$.

So there are

circles like this: $$(0)(d)|(d)(2d)|\cdots|(6d)(0)$$ for every $$d\in\mathbb{F}_7^\times$$.

Now just

connect all the circles, and insert the remaining $$7$$ tiles of the form $$(d)(d)$$ anywhere you like.

• @JaapScherphuis Well... upon carefully reading the question, it does say "Can you place ...". So perhaps you mean a better answer should be "yes I can, because $7$ is an odd number"? – WhatsUp Oct 24 '19 at 5:26