A roman walks into a bar, holds up two fingers, and says “Five beers, please.”

Everyone’s education in mathematics started with counting fingers. We have drifted from relying on fingers to count since then. But we can still catch ourselves using fingers to count stuff like telephone numbers.

The title says counting fingers, in the following paragraphs I’m going to teach you how to count to 1000 (Up to 1023 to be exact) using just the fingers on your hands. To be able to do this, you need to know a bit about binary numbers.

Binary number system has only one and zero, this can also be used to represent the two stages on or off. So how does this help with counting. Most you may have realized the connection when I said you can count from 0 to 1023. For those who didn’t follow, this picture might help?

Each finger from right to left can be used to represent numbers in powers of two.

Here is an example, try finding out the number represented here in this picture.

So from right to left, the right thumb is straight, the right ring finger and the little finger. So after giving the fingers the values each of them represent we get the number 00000 11001. Now let’s convert this to a number we are more familiar with: to a decimal number. Considering only the right hand its

(24x1)+(23x1)+( 22x0)+(21x0)+( 20x1 ) = (16×1)+(8×1)+( 4×0)+(2×0)+(1×1) = 25

Now try converting fingers in this picture, with all the fingers straight.

If your calculations are correct you should get 1023. So the largest number you can represent this way is that, 1023. And when you consider the state with all the fingers bent, like in picture 1. You represent zero. So zero along with other 1023 numbers let you show 1024 different numbers from 0 to 1023 just using your fingers.

Even though it’s a clever idea, it may have occurred to you that this isn’t that much of use in real life. Because peoples understanding of the binary numbers is not much, you can’t yet go around ordering 24 plates of spaghetti by holding up fingers.

When I told about this to my friends, they played around with their fingers for a while and before long they found out that certain numbers make funny or otherwise offensive combinations of fingers. So another disadvantage of this handy method is that people thinking that you are making rude hand gestures.

Have fun trying to find out which numbers make the rude hand gestures and which ones makes the Spiderman’s web throwing gesture.

P.S. The condition when people have six fingers instead of five in hand is called polydactyly, what’s the largest number a polydactyl person can represent, if they had twelve fingers in each hand and both extra fingers were equally flexible.

First published in: University of Colombo, Faculty of Science Blog.