## Friday, January 11, 2013

### An iAbacus Puzzle

As we are talking about shopping strategies in this week's newsletter I recollect that 30-35 years ago when I was a child most of the stores didn't have computerized cash registers but instead used wooden abacuses.  Remember this?

You can find those only in the thrift shops right now. In fact my mother-in-law presented me with one she bought at a thrift market in Georgia's mountains (not in the US).
Ikea sells a colorful children version that is a great math toy for babies as well as an addition friend for older kids.
My question is whether in our age of small gadgets you can make this abacus more miniature. And I don't mean smaller beans/buttons but rather using less of them. You should still be able to count to 1,000 and it shouldn't be too hard. Do you think it is possible?

Your answers accepted any time until midnight on Sunday on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Jerome said...

Here are all the various abacii (the correct plural I think) found throughout the world.

http://en.wikipedia.org/wiki/Abacus

I used to have two of them, both Japanese. My favorite was a collector's item made with a jade base and 7 columns of 1 brass bead on top and 4 on the bottom of a divider also made of brass. The frame was brass as well.

The other resembled the picture in the cited reference. The Japanese Soroban uses many fewer beads and works as follows (or it is the way I worked it.)

1. the starting position is the location of the beads when the abacus is put on the bottom edge (vertically). Each column represents a power of 10. To use the abacus, lay it flat after "zeroing" it.

2. Any number of 1 to 4 inclusive uses the bottom 4 beads. They are moved away from the bottom edge.

3. Five shifts all the bottom 4 beads to the starting position and puts the 5 up. The 5 is the single bead above the 4 lower ones.

4. Any number between 6 and 9 is represented by the 5 bead and the number of bottom beads to get to the number. For example 8 would be the single 5 bead and the 3 of the 4 bottom beads.

I don't know how a Russian Abacus works but that is the kind that is shown in your picture.

Oddities
========
1. below is an abacus that is built as a pair of cufflinks. I have no idea how it works, but it might be nice as a gift for someone who is a male and mathematical.

2. When you search on ebay for abacii, a whole pile of references come up for Jewelery made mostly in Cnina. I don't know if these are abacii or whether they are just a style of jewelery and I shouldn't be listing them at all. However, some would make nice gifts for females who are mathematical.

3. A soroban can be found on ebay, along with a Russian Winnie the Pooh abacus.

4. I think, but don't quote me on this, that there is a scene in the movie INFINITY, a very good biography of Richard Feynman, where Feynman was shown trying to find the cube root of a number in his head, while the person he played this game with was using an abacus. I don't remember what kind (Chinese likely), but both of them were enjoying the competition.

Anonymous said...

Maria,
The abacuses(plural?) you pictured are in base 10. The Japanese use one with a base of 5 called a soroban that uses less beads. Maybe using base of one like using binary code would work but I am not sure how many bead that would take or how hard it would be to use. I think the least number of beads would be one that has a bead denoting 500 beads. 4 beads worth 100. 1 bead worth 50. 4 beads worth 10 and 10 single beads. 20 beads total.

Gurubandhu

Ilya said...

I have a mental block on this one. The only idea that came to mind is to paint each bean's half dark an half light color, so by turning it you either see dark or light. Dark would represent 2 units, and light 1. That way you only need 5 beans in each row. It's not terribly complicated to use, but takes some extra time to turn each bean as needed, and a bit more "mental strain".

Maria said...

Soroban - exactly what I had in mind. I learned about it last week only and thought of sharing this cool super-abacus with you in my next week newsletter. But before - I wanted to challenge you to invent it in this week's puzzle.

Ilya kind of went there, but the rest of you seem to already be familiar with Soroban. Why didn't they tell us in Russia about it? We only saw standard 10-beed abacuses.

Jerome - thank you for the holiday gift suggestions. Very creative. I always forget about the eBay option and peculiar unique objects you can find there for not much. A puzzle point for each and I will share an interesting Soroban video in the next newsletter.