1. The problem is to understand Pascal's triangle and how to construct it. 2. Pascal's triangle is a triangular array where each number is the sum of the two numbers directly above it from the previous row. 3. The first row is simply $1$. 4. From the second row on, the edges of the triangle are always $1$, and each interior number is calculated as $$\text{value} = \text{above left} + \text{above right}.$$ 5. For example, the first few rows are: $$ \begin{array}{ccccccc} &&&1&&& \\ &&1&&1&& \\ &1&&2&&1& \\ 1&&3&&3&&1 \\ \end{array} $$ 6. Pascal's triangle also represents binomial coefficients such that the $n^{th}$ row corresponds to coefficients in the expansion of $(a + b)^n$. 7. For example, row 3: $1, 3, 3, 1$ corresponds to $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$. 8. Each element can also be computed using combinations as $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ where $n$ is the row number starting at 0 and $k$ is the position in the row starting at 0. 9. Pascal's triangle is widely used in combinatorics, probability, and algebra.