Three pentagram-shaped stars (the stars formed from the diagonals of a regular pentagon) are stacked up so that the bottom two ends of the tips touch the middle ends of the tips of the star below. (See diagram.)

The distance from the top of the stack to the floor (where the bottom star's "feet" rest) is 4 feet.

What is the distance between the bottom two ends of the tips of the stack that touch the floor?

This problem has had three respondents offer the same distance but we've had no joy in having confirmation.

Therefore I can only conclude that Gamer has either a specific method of solution that none have addressed or else we have read the problem incorrectly.

Revisit the second paragraph of the problem's text.  The assumption has been that the 4 ft is a vertical distance, but is the meaning that of the oblique distance from the apex of the structure to 'where the bottom star's "feet rest'?

I did evaluate this proportionally, ie, I used the vertical height of 4 ft and half my calculated base to calc the hypotenuse of apex to 'foot'.

This gave me a slightly shorter distance than my earlier solution, but this value is floating around somewhere in my system so I can't provide it immediately.

Gamer, is this how we should have read the story?

Posted by brianjn on 2005-03-08 08:56:49