You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system
A rectangular board has 10 columns and is numbered in a similar manner to a chessboard, beginning in the upper left corner and moving left to right. A student shades square 1, then skips one square and shades square 3, skips two squares and shades square 6, skips three squares and shades square 10, and continues this pattern of skipping \(n\) squares (where \(n\) is the step number starting from 0) before shading the next square. Determine the number of the shaded square that first results in having at least one shaded square in each of the 10 columns.
user
136
rule
A rectangular board has 10 columns and is numbered in a similar manner to a chessboard, beginning in the upper left corner and moving left to right. A student shades square 1, then skips one square and shades square 3, skips two squares and shades square 6, skips three squares and shades square 10, and continues this pattern of skipping \(n\) squares (where \(n\) is the step number starting from 0) before shading the next square. Determine the number of the shaded square that first results in having at least one shaded square in each of the 10 columns.
train