Unit 11 · Algebraic / Equation Reasoning
Folded String Marks — How Long Is It?
Lesson 4 of 4
About this lesson
What happens to a string when you fold it repeatedly and mark the midpoint each time? This question looks like it might need spatial imagination — but really it is a pure procedure-tracking problem. Each fold doubles the number of layers, so one mark through the bundle creates twice as many marks as the fold before it. Count the marks, count the segments, set up one simple equation. Done.
Chapters
Question
A piece of string is initially held end-to-end in a straight line. A mark is made in the middle of the string. The string is then folded in half and the new ends again pulled tight. A mark is made in the middle of the strands of folded string. This process is then repeated a third time.
The string is then unfolded and its ends pulled so that it is once again in its initial straight line.
The distance between marks on the string is found to be 4 cm.
How long is the piece of string?
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