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 John von Neumann 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.

Henry Ernest Dudeney, giving the answer to this problem based in a different context, reports that a French professor of mathematics exclaimed:

"Mon Dieu, quelle série!"

also completely overlooking the simple manner of solution.

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

That is:

$\ds 20 \times 2 \sum_{n \mathop \ge 1} \paren {\frac 1 3}^n = 20$