Monday, March 23, 2009

5-star challenge #4

Grades 11 & 12 5-Star Challenge #4
Captain Cooke the buccaneer buried his treasure at a small Himalayan boarding school. His legendary love of mathematical riddles inspired him to leave this clue, enigmatically encoded in the arrangement of 216 enormous stainless steel cuneiform characters in the school’s Peace Garden:

"The treasure is below Handsome Field. Start at the pile of broken tube-lights. Walk straight to the rock that looks like a flower, counting your steps. Turn 90 degrees to the right and walk the same number of steps in that direction. Put a twig in the ground where you stop. Start again at the pile of broken tube-lights and walk directly to the flower that looks like a rock, counting your steps. Turn 90 degrees to the left and walk that number of steps in that direction. Stick a twig in the ground at that point. Tie twine tautly 'tween the twain twigs and find its halfway point. The treasure is buried beneath the midpoint of the twine."

Centuries later, the clue is discovered by a visiting alumna as she ponders the 5-Star Challenge #971. After decoding the directions, the alumna rushes down to the Handsome Field Coliseum (via the Class of 2009 Memorial Escalator) to discover that the flower and the rock are still inexplicably in their places, but the pile of broken tube-lights has been removed without a trace by CLEAN! Without knowing where the broken tube-lights should be, and without digging at random all over Handsome Field, is it still possible for the alumna to find Captain Cooke's treasure? Explain.

Grades 9 & 10 5-Star Challenge #4
Point A is 6 units from the center of a circle of radius 10. How many chords of the circle have integral length and pass through point A?

3 comments:

  1. I read Grades 11& 12 5-Star Challenge #4 in one of my favorite books many years ago, "One, Two Three Infinity..." Although I can no longer remember the answer so I am trying to decide if it would be easier to solve the problem or find the book.

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  2. Wouldn't it be directly beneath the rock that looks like a flower?

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  3. I believe the answer to the second question is 8. The chords have lengths 20, 19, 19, 18, 18, 17, 17, and 16.

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