Treasure Map

Adapted from:

"One, Two, Three, Infinity" by George Gamow

       

There once was a young adventurous man who found among his great-grandfather's papers a piece of parchment that claimed to

reveal the location of a hidden treasure.  The instructions read:

 

Sail to 17º North latitude and 88 º West longitude where thou wilt

find a deserted island.  There lieth a large meadow, not pent, on the

north shore of the island where standeth a lonely oak and a lonely

pine.  There thou wilt see also an old gallows on which we once

were wont to hang traitors.  Start thou from the gallows and walk

to the oak counting thy steps.  At the oak thou must turn right by

a right angle and take the same number of steps.  Put here a spike

in the ground.  Now must thou return to the gallows and walk to

the pine counting thy steps.  At the pine thou must turn left by a

right angle and see that thou takest the same number of steps,

and put another spike into the ground.  Dig halfway between the

spikes; the treasure is there.

 

The instructions were quite clear and explicit, so the young man chartered a ship and sailed to the location and found the island.

He also found the field and the oak and the pine, but to his great sorrow the gallows was gone.  Too long a time had passed since the

treasure map had been written; rain and sun and wind had disintegrated the wood and returned it to the soil, leaving no

trace even of the place where it once had stood.

 

The young man fell into despair, then in an angry frenzy began to dig at random all over the field.  But all his efforts were in

vain; the island was too big.  So he sailed back home with empty hands.  And the treasure is probably still there.

 

Find the treasure:

 

One approach

 

Put the trees anywhere on a sheet of paper.

 

  1. Plot the trees anywhere on a sheet of paper (or use appropriate technology).
  2. Place the gallows anywhere you want
  3. Locate the “X” using information from the instructions.
  4. Do it again for several gallows and tree locations.
  5. Is there a pattern to the position of the “X” versus the location of the trees or gallows?
  6. Can you prove this?