solution: By the associative property of multiplication, it doesn't help to insert parentheses that specify the order of multiplication. For example, the associative property tells us that $(2\cdot(3\cdot 4))\cdot (5+1)$ is the same as $2\cdot3\cdot4\cdot (5+1)$. So the only way to get different values is to group +1 with a different number of factors. We get \begin{align*}
  2\cdot 3 \cdot 4 \cdot (5 + 1) &= 144, \\
  2\cdot 3 \cdot (4 \cdot 5 + 1) &= 126,\\
  2\cdot (3 \cdot 4 \cdot 5 + 1) &= 122, \\
  (2\cdot 3 \cdot 4 \cdot 5) + 1 \hphantom{)} &= 121.
  \end{align*}In total there are $\boxed{4}$ possible values for the expression.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  The expression $2\cdot 3 \cdot 4\cdot 5+1$ is equal to 121, since multiplication is carried out before addition. However, we can obtain values other than 121 for this expression if we are allowed to change it by inserting parentheses. For example, we can obtain 144 by writing \[
  (2\cdot (3\cdot 4)) \cdot (5+1) = 144.
  \]In total, how many values can be obtained from the expression $2\cdot 3\cdot 4 \cdot 5 + 1$ by inserting parentheses? (Note that rearranging terms is not allowed, only inserting parentheses).
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 4
extra_info.question: The expression $2\cdot 3 \cdot 4\cdot 5+1$ is equal to 121, since multiplication is carried out before addition. However, we can obtain values other than 121 for this expression if we are allowed to change it by inserting parentheses. For example, we can obtain 144 by writing \[
  (2\cdot (3\cdot 4)) \cdot (5+1) = 144.
  \]In total, how many values can be obtained from the expression $2\cdot 3\cdot 4 \cdot 5 + 1$ by inserting parentheses? (Note that rearranging terms is not allowed, only inserting parentheses).
extra_info.split: test