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If this match stick pattern continued, how many match sticks would be needed for the 100100th shape?

Question

If this match stick pattern continued, how many match sticks would be needed for the 100100th shape?

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Solution

To answer this question, I need to know the pattern of the match stick shapes. The pattern could be linear, quadratic, or something else. Once I know the pattern, I can use it to calculate the number of match sticks needed for the 100100th shape.

For example, if the pattern was linear and each new shape required 2 more match sticks than the previous one, I would calculate it like this:

  1. Find the number of match sticks in the first shape. Let's say it's 2.
  2. Since each new shape requires 2 more match sticks, the 100100th shape would require 2*100100 match sticks.
  3. So, the 100100th shape would require 200200 match sticks.

But without knowing the pattern, I can't give a specific answer.

This problem has been solved

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