Visualizing this method can make calculating very easy.

only japanese could do this ....

great, but how about multipling with 0 (e.g. 103X120??)
also 99X99 seems so dizzy...

Damn! Now why didn't we have that when WE were kids!

Very clever those Japanese chappies!

#3 Pretty simple really. I had no idea but running a simple 10x10 example made it clear.

Draw lines as you would normally for each digit space. For 0, make a single line but mark it in some way (I made it look squiggly).

Count the dots as you would normally but only for the straight lines. If any dots are touching the squiggly lines, disregard them completely.

Ta-dah!


For the 10x10 example it's like that:

left: 1 intersection, both straight lines = 1
mid: 2 intersections, both touching the squiggly line = 0 + 0 = 0
right: 1 intersection, both lines are squiggly = 0

#6 you made my head hurt

Very long winded method of multiplying large numbers, If you haven't got a calculator it's far far easier to use the stack and carry method plus you haven't got to forget when you haven't used the line system for a while whether to start your second lot of lines at the bottom or the top. Not to mention remembering to count from right to left as apposed to left to right. Not wishing to alienate myself from any Japanese people, but my guess is that this was only used by the uneducated, perhaps farm workers etc.

#7 Apologies. I'll use a lighter hammer next time.