There is a strange circular disk on a table. It has twelve congruent sectors, each of which is either opaque or transparent.

An identical disk is placed on top of it, and spun around. The table underneath the disks is brightly colored, so that every 30 degrees of rotation, you can count the number of regions out of 12 that are transparent. Those numbers are 2, 3, 4, 4, 0, and 4 for the first half of a revolution. Without any more information, can you figure out exactly what a single disk looks like?

One can consider the pattern of 12 sectors to be digits in a 12 digit binary number.   1 for transparent, 0 for opaque.

A second number is generated by multiplying the first number by 2 and then replacing the zero in the 1's column by the 13th digit.

"AND"ing the digits of the first and second number will give a third number; summing it's digits gives the number of transparent regions that show through.

Repeat the 'multiply and wrap' step to make a new "second number" from the old second number.  Repeat the AND and sum step etc

I'll leave the rest to the programmers.
But I wonder if there is a more analytical method...

Posted by Larry on 2005-12-03 12:20:23