# math

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A fireman stood on the mioddle step of a ladder, shooting water into a burning building . As the smoke lessened, he climbed up three steps and continued his work. the fire got worse,so he had to go down five steps. Later he climbed up the last six steps and was at the top of the ladder. How many steps wre there?

• math -

If he stepped on the middle step, there must be an odd number of steps, say 2n+1.
He started off at step n+1.

"he climbed up three steps"
he was on step n+1+3.

"go down five steps"
he was on step n+1+3-5.

"climbed up the last six steps and was at the top"
n+1+3-5+6=2n+1
solve for n, and the number of steps is 2n+1.

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