Problem C

Domi Knows

A domino tile is a rectangular tile with a line dividing its face into two square ends. Each end is marked with a number of dots (also called pips) or is blank.

The first domino shown below is a \([3,5]\) domino, since there are \(3\) pips on its left end and \(5\) pips on its right end. The second domino shown below is a \([0,3]\) domino, since there are \(0\) pips on its left end and \(3\) pips on its right end. The third domino shown below is a \([4,4]\) domino, since there are \(4\) pips on its left end and \(4\) pips on its right end.

We can also rotate the domino tiles. The first domino shown below is a \([5,3]\) domino, since there are \(5\) pips on its left end and \(3\) pips on its right end. However, since this tile can be obtained by rotating the \([3,5]\) tile, \([5,3]\) and \([3,5]\) represent the same domino. Similarly, the second domino shown below is a \([3,0]\) domino. Again, note that \([3,0]\) and \([0,3]\) represent the same domino.

A \(2\)-set of dominoes contains all possible tiles with the number of pips on any end ranging from \(0\) to \(2\), with no two dominoes being the same. A \(2\)-set of dominoes has the following six tiles: \([0,0]\), \([0,1]\), \([0,2]\), \([1,1]\), \([1,2]\), \([2,2]\). Notice that the three dominoes \([1,0]\), \([2,0]\), and \([2,1]\) are not listed because they are the same as the three dominoes \([0,1]\), \([0,2]\), and \([1,2]\).

Similarly, a \(12\)-set of dominoes contains all possible tiles with the number of pips on any end ranging from \(0\) to \(12\), with no two dominoes being the same.

Domi purchased a \(12\)-set of dominoes. How many tiles are in the set?

**Theme:** Number Sense