The Bulldozers and the Bee/Historical Note

Historical Note on The Bulldozers and the Bee
The problem of The Bulldozers and the Bee has been phrased in several different forms.

One many apocryphal tales concerning is that he was asked this question. He instantly gave the answer.


 * "So you've heard this one then? You solved it the quick way?" he was asked.


 * "I solved it by summing an infinite geometric progression. There's a quicker way?" was the reply.

The point is that there are (at least) two ways to solve the problem, and they come to the same value.

That is:
 * $\displaystyle 20 \times 2 \sum_{n \mathop \ge 1} \paren {\frac 1 3}^n = 20$