athematicians have a passion for balls. Colored balls, usually. Or numbered balls. Imaginary balls, of course, for they are most useful in a thought experiments, such as this one...

• At one minute to midnight, a mathematician placed ten balls, numbered one through ten, into a vase and removed the ball marked with the number one. 
• At one-half of a minute to midnight, the mathematician placed ten more balls, numbered eleven through twenty, into the vase and removed number two. 
• At one-third of a minute to midnight, the mathematician placed ten more balls, numbered twenty-one through thirty, into the vase and removed number three. 
• At one-fourth of a minute to midnight,...