This is a guest post by Danielle
I learned this problem from The Puzzler’s Elusion (flipkart link) by Dr. Dennis E. Shasha. It’s called Polish Hand Magic. It’s not a method of counting faster, but it is a fun little trick to show young kids (and adults) who know their multiplication tables.
In this Magical Polish tradition, a closed fist equals 5. Let’s say you want to multiply 7 x 8.
7 is represented by …||, or three fingers down and two up. 8 is represented by ..|||, or two fingers down and three up. Find the sum of the fingers that are up, in this case, the amount of vertical lines. Then multiply the number of finger down. So:
…|| and ..|||
2 + 3 fingers up = 5
3 × 2 fingers down = 6
Bada bing! The answer: 56
If you want to multiply 6 x 9 you have ….|(six) and .||||(nine)
1 + 4 fingers up = 5
4 × 1 fingers down = 4
The answer is 54!
Okay, so it works! But do you know how? Try thinking about it for five minutes before scrolling down to the answer.
10 [(x-5) + (y-5)] 1 [(10 – x) × (10-y)]
_______________ + _________________
10 times sum of 1 times product
Values of down values
= 10x + 10y – 10x – 10y + x – y
= X × Y
Try doing this problem with larger and smaller numbers by imagining extra fingers and negative fingers.
Danielle is a young business litigation student who spends a lot of time on web sites like Tanga.com seeking deals to save her money and math games to keep her entertained. In doing so, she stumbled across Polish Hand Magic and tried it with her eight-year-old niece, Abbe. Her response? “Why don’t you just do it the easy way instead?”