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Question

A 94‐inch piece of pipe is to be cut at two points A and B such that A and B are not on the ends of the pipe and the length from A to B is 48 inches. How many possibilities are there for obtaining three pieces of pipe of different lengths if the lengths are whole numbers?
 

Answer 1

If the middle section from A to B is 48 inches long, then the two end sections add up to 94-48 = 46 inches.  The answer to the question is 46/2 = 23

 

  first              last

section         section

    1                 45

    2                 44

    3                 43

    4                 42

   ....               ....

   21                25

   22                24

   23                23

 

Once the first section goes to 24, the two sections start to repeat: 24 and 22, 25 and 21, etc.  Since A and B are not on the end, we can't have 0 for either the first or last section of the pipe.