Question 154
An ordinary domino set consists of 28 pieces. Each piece is formed by two integers ranging from $0$ to $6$, inclusive. All possible combinations $(a, b)$, with $a \leq b$, are listed exactly once. Note that the piece $(4,2)$ is listed as the piece $(2,4)$, since $2 \leq 4$. Excluding the piece $(0,0)$, for each of the other 27 pieces $(a, b)$, with $a \leq b$, we write on a board the fraction $\frac{a}{b}$.
a) How many distinct values are written in the form of fractions on the board? (Note that the fractions $\frac{1}{2}$ and $\frac{2}{4}$ have the same value and must be counted only once.)
b) What is the sum of the distinct values found in the previous item?
a) How many distinct values are written in the form of fractions on the board? (Note that the fractions $\frac{1}{2}$ and $\frac{2}{4}$ have the same value and must be counted only once.)
b) What is the sum of the distinct values found in the previous item?