1. **State the problem:** Pedro creates patterns of dominoes with dots. Each pattern has a certain number of dominoes and dots. We want to find which pattern number corresponds to a total of 124 dots. 2. **Analyze the patterns:** - Pattern 1: dominoes are [1|6], [1|4], [1|6]. Number of dominoes = 3. - Pattern 2: dominoes are [1|6], [2|4], [2|4], [1|6]. Number of dominoes = 4. - Pattern 3: dominoes are [1|6], [2|4], [2|4], [2|4], [1|6]. Number of dominoes = 5. 3. **Count dots per domino:** - [1|6] has $1+6=7$ dots. - [1|4] has $1+4=5$ dots. - [2|4] has $2+4=6$ dots. 4. **Dots in each pattern:** - Pattern 1: two [1|6] dominoes and one [1|4] domino. Total dots = $7 + 5 + 7 = 19$ - Pattern 2: two [1|6] dominoes and two [2|4] dominoes. Total dots = $7 + 6 + 6 + 7 = 26$ - Pattern 3: two [1|6] dominoes and three [2|4] dominoes. Total dots = $7 + 6 + 6 + 6 + 7 = 32$ 5. **Generalize the pattern:** - Number of dominoes in pattern $n$ is $n + 2$. - Each pattern starts and ends with [1|6] dominoes (2 dominoes total). - The middle dominoes are [2|4], and their count is $n - 1$. 6. **Formula for total dots in pattern $n$:** $$\text{Total dots} = 2 \times 7 + (n - 1) \times 6 = 14 + 6(n - 1) = 14 + 6n - 6 = 6n + 8$$ 7. **Find $n$ for total dots = 124:** $$124 = 6n + 8$$ $$124 - 8 = 6n$$ $$116 = 6n$$ $$n = \frac{116}{6} = \frac{\cancel{116}}{\cancel{6}} = \frac{58}{3}$$ Since $n$ must be an integer pattern number, check if 124 dots is possible exactly. 8. **Check integer $n$:** $\frac{58}{3} \approx 19.33$, not an integer. Try $n=19$: $$6 \times 19 + 8 = 114 + 8 = 122$$ dots. Try $n=20$: $$6 \times 20 + 8 = 120 + 8 = 128$$ dots. 9. **Conclusion:** 124 dots is not possible exactly with this pattern rule. If the problem expects the closest pattern number, $n=19$ gives 122 dots, $n=20$ gives 128 dots. **Final answer:** The pattern number closest to 124 dots is $n=19$ with 122 dots or $n=20$ with 128 dots. **Pattern rule:** Total dots in pattern $n$ is given by $$6n + 8$$ where $n$ is the pattern number starting from 1.