[["Problem: The base-10 integers 36, 64, and 81 can be converted into other bases so that their values are represented by the same digits $\\triangle\\Box\\Box$, where $\\triangle$ and $\\Box$ are two distinct digits from 0-9. What is the value of $\\triangle\\Box\\Box$?\nAnswer:",["\n"]],["Problem: Find the modulo $7$ remainder of the sum $1+3+5+7+9+\\dots+195+197+199.$\nAnswer:",["\n"]],["Problem: The number of apples that Sophia has is a multiple of $6$. When she sells one apple, the number of apples is a multiple of $n$. If $n$ is a positive integer less than $10$, how many possible values are there for $n$?\nAnswer:",["\n"]],["Problem: Find the remainder of $7^{17}$ when it is divided by 5.\nAnswer:",["\n"]],["Problem: Arnold must water his cactus plants every 9 days and he must feed them every 60 days. He watered and fed them last Tuesday. What day of the week will it be the next time he waters and feeds them on the same day?\nAnswer:",["\n"]],["Problem: What digit must be placed in the blank to make the four-digit integer $20\\_7$ a multiple of 11?\nAnswer:",["\n"]],["Problem: A group of $N$ students, where $N < 50$, is on a field trip. If their teacher puts them in groups of 8, the last group has 5 students. If their teacher instead puts them in groups of 6, the last group has 3 students. What is the sum of all possible values of $N$?\nAnswer:",["\n"]],["Problem: What is the units digit of $3^1 + 3^3 + 3^5 + 3^7 + \\ldots + 3^{2009}$?\nAnswer:",["\n"]],["Problem: When all the girls at Madeline's school line up in rows of eight, there are seven left over.\n\nIf instead they line up in rows of four, how many are left over?\nAnswer:",["\n"]],["Problem: Convert $222_{10}$ to base $13$. Use digits A, B, and C if necessary.\nAnswer:",["\n"]]]
