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how to fold a duck in 8 steps from a 24 cm x 24 cm piece of paper

Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 2 E12 E+9

December 12, 2022
geometry

Problem Statement

Csongi taught Benedek how to fold a duck in 8 steps from a 2424 cm ×24\times 24 cm piece of paper. The paper is meant to be folded along the dashed line in the direction of the arrow. Once Benedek folded the duck, he undid all the steps, finding crease lines on the square sheet of paper. On one side of the paper, he drew in blue the folds which opened towards Benedek, and in red the folds which opened toward the table. How many cm is the difference between the total length of the blue lines and the red lines? https://cdn.artofproblemsolving.com/attachments/0/1/358a3b2c3b959a85406b94e34c182fd1c2e28d.png