Three Finger Tricks for Multiplying also made me think of another finger trick: using both hands to count to 99. It’s not as clever as multiplication, but it’s one I use regularly for keeping track of numbers and for simple addition or subtraction.
The idea is simple: the left hand keeps track of tens while the right hand keeps track of units. On the left hand, the thumb is worth 50 and each of the other fingers is worth 10. Likewise, on the right hand, the thumb is worth 5 while each of the other fingers is worth 1. This picture (below) shows 27:
while this picture (below) shows 67:
I first learned this in 2nd grade, when it appeared as an article in my Weekly Reader magazine. The article mentioned that this method was used by children in Asia (as it mimics an abacus) and that it could even be modified for addition, subtraction, and multiplication. Addition and subtraction seem straightforward, in the sense that the hands can be used to keep a running tally, but I have yet to figure out how multiplication would be done. [Indeed, having taught multiplication on an abacus, I feel like I would need to grow several more hands before I could apply that technique].
Still, for keeping track of 2-digits numbers, it’s simple and definitely memorable!
360 
January 5, 2008 at 11:30 am |
Cool stuff! A nice finesse to have each hand represent digits from 0 to 9, tasting a bit like egyptian or roman techniques for representing groups of 0 to 9.
When asking students to count on their fingers, if you suggest they can go past ten, they often come up with a base five process: count ones on the right hand, and groups of five on the left, leading to representations of numbers from 0 to 30. But in fact, with symbols for 0 to 5 available on each hand, a base six numeration is more natural here, leading to numbers from 0 to 55 (base six), that is, 0 to 35.
But the winner in the number representation contest is base two. Regarding each finger as a digit, we get base two numerals from 0 to 1111111111 (that is, 0 to 1023).
September 15, 2009 at 7:13 am |
Hi! Found your blog via your visualisation of extracting square and cube roots, and then noticed this page as I was browsing. Nice!
Glad to see a reference to counting in binary on one’s fingers. I’ve done this since I started playing double bass in an orchestra. Bassists sometimes have long rests between their entries, but counting on two hands obviously means putting down your bow. This is a bad idea: one, it looks sloppy; two, you can miss your next entry if you miscount and suddenly spot the conductor frantically cueing you. It takes a bar (measure) or so to pick up and reposition your bow, especially if you are to avoid a loud “crack” as the flailing bow hits the stand or your bass in the process, which sort of spoils the magic of a concert!
Anyway, I worked out that I could count up to 31 bars on my left hand without taking this risk. Once I got the hang of it, I could do it without thinking and actually listen to the orchestra during my own rest!
(Plus it’s an excellent way of counting paces if you need to keep track of how far you’ve walked in poor visibility. Count double paces and you can keep counting for more than a kilometre.)