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There are five pieces of blue string on the table with different lengths, the total length of which is 30 cm. There are also five pieces of red string with different lengths, the total length of which is 30 cm.
Is it possible to cut these pieces of string so that in the end they can be divided into pairs so that the length of the strings is equal in each pair and their color is different?

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    $\begingroup$ Is this a puzzle you found elsewhere? If so, please edit your source in, as we have an attribution policy - unsourced puzzle may be closed. $\endgroup$
    – bobble
    Jan 5, 2021 at 17:13

1 Answer 1

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Yes. Just line up the strings end to end for each color, and make a cut for one color wherever the endpoints meet for two consecutive strings of the other color. (A "common refinement" of the two partitions of the interval $[0,30]$.)

Before: enter image description here After: enter image description here

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  • $\begingroup$ Could you please explain more.. I did not understand $\endgroup$ Jan 5, 2021 at 17:11
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    $\begingroup$ @Reza I added pictures. $\endgroup$
    – RobPratt
    Jan 5, 2021 at 18:26
  • $\begingroup$ What if we have 3 pieces of the blue string... Could we again do this? @RobPratt $\endgroup$ Jan 5, 2021 at 19:53
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    $\begingroup$ @Reza, the number of pieces can differ between colors. The only requirement is that the total lengths are equal. $\endgroup$
    – RobPratt
    Jan 5, 2021 at 20:12

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