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Dear Mitch,

Is there any way you know to do the three-times table by using your fingers?

I really hope you do,

Victor Bardales


Dear Victor Bardales,

Sure, I can think of a way!

While I'm sure that if you search around enough and ask enough people you are bound to come up with a bunch of ways to do any of the times' tables using your fingers or some other easy technique or "trick," but here's one that came to me after thinking about your question for a little while:

First, think of your thumbs and "threes," which is easy to do, once you remind yourself that the word "thumb" and the word "three" both begin with "th."  Next, notice that when you ignore your thumbs for a moment, all your other fingers, when your palms are facing you, are divided up into three sections each: the fingertip at the top, the middle part of each finger, and the bottom third of each finger which connects to your palm.

Then, with both palms facing you, you begin at the left and count out the number by which you are multiplying by the number three, with one count for each finger.  In other words, if you are trying to calculate 4 x 3, beginning on your left hand, you count out one for the thumb, one for the forefinger, one for the middle finger, and one for the 'ring' finger, totaling 4 fingers.

Next, with the thumb standing for one of the threes (remember, the "th" in "thumb" gives the thumb its value of 3), and for the other fingers the value of three separate parts for the index finger (or 'first finger'), and the value of three for the three separate segments of the middle finger, derived from its 3 segments, and finally the set of three derived from the 'ring' finger, which also, of course, is comprised of three separate and distinct parts, all get added together to give us our total of 12.  And that, of course, is indeed the answer to the question, what does three times four equal?  TWELVE.

To recap, you now have four sets of three: the thumb, the first finger (with its three separate parts), the middle finger (with its three separate parts), and the ring finger (with its three separate parts).  And when you add them all up you should arrive at the sum of twelve.

This technique or "trick" will work equally well for all multiples of three up to and including ten.  After that, of course, you can return to your left-most thumb and continue adding on until you reach 3 x 12 or 3 x 15 or 3 x 20, etc., depending upon how many times you wish to add up segments of digits.

As far as I know, this is my own little realization, but if anyone out there has already publicly discussed or written about this lucky happenstance, by all means feel free to contact me and I will include your name.  

I hope this helps!

Mathematically yours,