Dominoes are rectangular tiles divided into two squares. Each square has a number $($usually

represented by a series of dots$)$ from $0$ to $6.$ A double$-$six set of dominoes has tiles of every

possible combination of these numbers, from $0-0$ to $6-6.$ Each possible combination of

numbers appears only once in a set, so a complete set of dominoes contains $28$ tiles. Two

tiles from a double$-$six set of dominoes are shown below:

In many games, you must place the dominoes next to each other in such a way that squares

with identical numbers are placed next to each other. Doubles are traditionally rotated

before they are placed. Adhering to these rules, the following shows a legal placement of

three dominoes:

Domino Placement Problem

Can all the dominoes in a double$-$six set be placed in a single line of tiles adhering to the

placement rules previously described? Can they all be placed so that the single line loops

back to the first domino? The remainder of this activity sheet will help you answer these

questions.

Decide how to use a graph to model the Domino Placement problem. Carefully define

what your vertices represent and how you know when two vertices are connected by an

edge.

Based on your model, restate the Domino Placement problem.

What type of previously solved problem in this unit is this problem related to$?$

Solve the Domino Placement problem.