SOLUTION: A 70-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 42 inches. How many possibilities are the

Question 1041842: A 70-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 42 inches. How many possibilities are there for obtaining three pieces of pipe of different lengths if the lengths are whole numbers?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I read the problem as:
The length AB never changes
So, length AB sits somewhere on the pipe
and there has to be lengths on both sides
so that I end up with 3 lengths
---------------------------
I can start off with lengths:
1, 42, 27
Keep adding 1 to the left side until I get:
2, 42, 26
3, 42, 25
4, 42, 24
5, 42, 23
6, 42, 22
7, 42, 21
8, 42, 20
9, 42, 19
10, 42, 18
11, 42, 17
12, 42, 16
13, 42, 15
14, 42, 14
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There are 14 different possibilities
( note that 15, 42, 13 is a repeat )

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