3050.11 – Fireman on the Ladder

A fireman stands on the middle rung of a ladder pouring water on a burning building. As the smoke clears he steps up 3 rungs. A sudden flare-up forces him down 5 rungs. Later he climbs up 7 rungs and stays there until the fire is out. At that point he climbs up the last 6 rungs (the top of the ladder touches the house just below the windowsill), and he enters the building.

How many rungs are on the ladder?


Draw a picture and act the scenario out. There are 23 rungs total and the fireman begins in the middle on rung #12.

Note: this problem was inspected and vetted by the staff at the Oberlin Fire Department. They told me that the scenario is valid. There is one slight change: for use with a two-story house, the ladder typically used is 24 feet long, and has 24 rungs, not 23. But for the sake of the problem it was agreed that 23 is OK--this gives a middle rung which the problem needs. Many thanks to the staff for their help.