Teaser Tuesday! July 22, 2014

Hope everyone enjoys this one! Should be a nice softball for the WSO crowd.

Note: If you could all please input your answers using the previously noted html code it will allow others to answer without having a spoiler. Seriously, just copy it verbatim and don't stick any " or ' in your answer and you'll be fine.

Question

Billy the banker recently took a personality test... he failed.

Actually, the test was set up so he couldn't fail. There were four personality "colors", and the objective was to decide which color was strongest in him. There were three test sections, and in each section, he had to rank the four colors from 1 (weakest) to 4 (strongest).

At the end of the test, he summed up the rankings from each section to get his personality "profile". The minimum he could score on any color was therefore 3, and the maximum was 12. After he knew how he scored for each color, the test asked him to color in a circle (with crayons) in proportion to his color scores.

Billy the banker complained that he didn't have a protractor to measure out the exact angles. (I wonder what this says about his personality?) He then remarked loudly that the test makers could have divided up the circle beforehand (pie-chart style) and then he would only have to color between the lines. The natural question is, of course: What is the minimum number of divisions that must be made so that the circle can be colored to accurately represent any possible proportion of colors? How are these divisions arranged?

Good luck!