« Where is spring? | Main | St Patrick for Ireland »

March 17, 2006

Regula Stultorum (Fools' Rule)

Regula Stultorum comes in quite handy if you want to multiply two numbers between 5 and 10 but can't remember the multiplication tables you've learnt by heart as a kid. Let's try for example 6 times 9. Raise as many fingers on each hand as the excess of each number above five and leave the others folded down. This should be 1 finger of your left and 4 fingers on your right hand. The raised fingers now represent the tens of the result, 5 x 10 = 50. The product of the fingers down on each hand gives 1 x 4 = 4. Therefore, the result of 6 x 9 = 50 + 4 = 54. Now try 7 x 7. That's two fingers up on each hand representing a value of 40. The multiplication of three fingers down on each hand is 3 x 3 = 9. So, 7 x 7 = 49. Dead easy, isn't it?

When you have sorted out your fingers again try 6 x 6. At first sight this does not seem to work as the raised fingers represent a value of only 20! But of course four fingers down on each hand mean 4 x 4 = 16. Phew! And now the ultimate test: 5 x 10 = ?

Believe it or not this system is still in use in some parts of the world, e. g. Syria, Palestine, Italy, Spain, southern France and southern Russia. Mathematically it is described by the following equation:

(5 + a)(5 + b) = 10(a + b) + (5 - a)(5 - b)

'a' and 'b' are the number of fingers we raise on each hand.

If your fingers have got cramped during these exercises you can use a slightly different approach which is called the complementary method. It was quite popular in the 16th century and is based on the same principles as the Regula Stultorum.

6   4         7   3
  X             X  
9   1         7   3
-------         -------
5   4         4   9

In the first column you write the numbers you want to multiply, 6 and 9 in the first example. The second column contains the difference of these numbers to ten. The tens are now found as the difference between either number and the >em>complement of the other number: (6 - 1) = (9 - 4) = 5. The unit digit is of course the product of the complements: 1 x 4 = 4. Not surprisingly the result is 54!

Coming to think of it it's a real pity I never learnt these things at school. I certainly would have got a lot more fun out of my maths lessons than I actually did.

Posted by Mausi at March 17, 2006 09:16 PM

Trackback Pings

TrackBack URL for this entry:


That is awesome. I never knew this one. I learned shortcuts for multiplying 9 with anything 1 to 9 and multiplying 11 by anything between 11 and 19... but this was new. Thank you!

Posted by: vw bug at March 17, 2006 05:39 PM