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Rope Escape

Puzzle

Rajeev is trapped atop a building 200m high. He has with him a rope 150m long. There is a hook at the top where he stands. Looking down, he notices that midway between him and the ground, at a height of 100m, there is a ledge with another hook. In his pocket lies a Swiss knife. Hmm... how might he be able to come down using the rope, the two hooks and the Swiss knife?

Source

Heard from Aristides Gionis sometimes in 2000 when we shared an office. Requires some lateral thinking!

Solution

Cut rope into 50m and 100m pieces. Tie one end of the 50m piece to the top hook and make a knot at the other end (see picture for a bowline knot) with a fixed loop. Pass the 100m piece through the loop and tie its two ends to form a loop. Now, Rajeev can climb down 100m to the ledge. Now, cut the 100m loop using the knife. Collect this piece by holding one end, pulling at it and letting the other end slide through the loop. Finally, tie one end of this 100m piece to the hook at the ledge and slide down.

Previous Puzzle: Pebble Piles

You are given three piles with 5, 49 and 51 pebbles respectively. Two operations are allowed: (a) merge two piles together or (b) divide a pile with an even number of pebbles into two equal piles. Is there a sequence of operations that would result in 105 piles with one pebble each?

Next Puzzle: Cake Cutting

Mary baked a rectangular cake. Merlin secretly carved out a small rectangular piece, ate it and vanished! The remaining cake has to be split evenly between Mary's two kids. How could this be done with only one cut through the cake?

12 Aug 2008
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