Wednesday, 25 May 2011

Two Ladders Puzzle

This puzzle is an old favourite of mine. It looks quite straightforward but it's not as easy as one might expect.

Two ladders are leaning against opposite walls in an alleyway. The bottom of each ladder is placed on the ground in the opposite corner. One ladder is 4m long, the other is 3m long. The height at which the two ladders meet is 1m.

Question: How far are the walls apart?


  1. This comment has been removed by the author.

  2. @Aaron sqrt(143/17)+sqrt(143/10) = 6.68
    That would make both ladders fall down. Sorry :(

  3. assuming the walls are perpendicular to the floor^2%29+%2B+1%2Fsqrt%2816-d^2%29

  4. solve: 1/sqrt(9-d*d) + 1/sqrt(16-d*d) = 1
    answer: d = 2.6032877544