### Let Your Digits Do the Multiplying

by James Tanton

In the “Problem Circle” section of the Summer/Fall 2015 MTCircular, James Tanton shared a finger-counting challenge. For those who want to use their toes, too, or who are curious about extraterrestrial finger multiplication, please check out Tanton’s additional challenges below.

#### Fingers and Toes

One can compute higher products using the same method with fingers and toes!

Two hands with all fingers down represents ten, as does two feet with all toes “down.” To compute 17 x 18, say, raise seven fingers to represent ten plus seven, and raise eight toes for ten plus eight.

Since we’re working with twenty fingers and toes, each raised digit is now worth 20. We currently have 15 digits up and that makes 300. Multiply the digits down, 3 and 2, to get the answer: 17 x 18 = 300 + 3 x 2 = 306

Why does this work?

#### Extraterrestrial Multiplication

Martians happen to have six fingers on each of two hands. What is the Martian version of this finger multiplication trick?

Venutians have two hands: one with four fingers and one with seven fingers. Is there a Venutian version of this finger trick?

And Plutonians have three hands, each with five fingers. Is there a Plutonian version of this method for triple products?

#### Comment

This finger multiplication trick has been bandied about for decades. I am not sure of its origin. Extensions to fingers and toes and to extraterrestrial products seem like natural next questions.