Are you confused?
If the toothpick numeral system puzzles you, don’t feel bad. It’s awkward. It’s impractical for expressing
gigantic numbers. People aren’t used to counting in blocks of five or fifty or five hundred. It’s easier to go
straight from blocks of one to blocks of ten, and then from ten to a hundred, then to a thousand, then to
ten thousand, and so on. But using blocks of five, fifty, five hundred and so on, in addition to the tradi-
tional multiples of ten, conserves toothpicks.
Here’s a challenge!
Using toothpick numerals represent the number seven hundred seventy-seven in two different ways. Make
sure one of your arrangements is the most “elegant” possible way to represent seven hundred seventy-
seven, meaning that it uses the smallest possible number of toothpicks.
Solution
Figure 1-3 shows two ways you can represent this number. In order to represent five hundred, you build
the F and the H together so they’re a single connected pattern of sticks. The arrangement on top is the
most “elegant” possible numeral.
You can represent seven hundred seventy-seven in more ways than just the two shown here. You can
make numerals that are far more “inelegant” than the bottom arrangement. The worst possible approach
is to lay down seven hundred seventy-seven toothpicks side-by-side.
Fingers and Sticks 51 5101050(^100253)
74
Figure 1- 2 Toothpick-numeral equivalents
of some numbers. In this system,
most numbers can be represented
by more than one numeral. But
there is always a “best numeral”
that uses the smallest possible
number of toothpicks.