Simplified abbacus

One of the problems I have with attempting the mental abbacus method is that I find it difficult to distinquish between 3 and 4 beads. So I imagined it would be a good idea to experiment with a simplified version of the abbacus. I don’t know if what I have come up with is original, so if any abbacus expert on this forum knows if it is, please let me know.

  • Just like with a normal abbacus, the right column is for the single digit numbers and the second column from the right is for tens;
  • You can only use 2 beads and/or an orange (or choose favorite color) card representing repectively 1 and 5 each;
  • 1/2 = 1/2 bead(s) at the bottom of square a; 3/4 is 2/1 beads at the cealing of square a (so 3 = 5 - 2 and 4 = 5 - 1); 5 is a card; 6/7 = 1/2 bead(s) at the bottom of square b; 8/9 is 2/1 beads at the ceiling of square b (8 = 10 - 2, etcetera).

I have not completely found out all the strategies you need to use for doing calculations, but I plan on working on that in the future.

Annyway, I would appreciate any kind of input on this system.

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I imagine that in order to do fast mental calculations with this system (or any other abbacus system) you need to be able to do the basic moving of beads without thinking in actual numbers.

Here are some hacks:
1 + 1 = 2: You are allowed to pace 2 beads on top of eachother, so you just do that;
1 + 2 = 3: Stacking is not allowed, just imagine that the single bead pushes the 2 beats to the cealing and disappears;
1 + 3 = 4: the single bead and the lower bead of the 2 beads combo annihilate eachother;
1 + 4 = 5: imagine sliding a card between the 2 beads;
2 + 2 = 4: when 2 2-beads-combinations meet, they both try to go to the ceiling and crash in to oneanother, resulting 1 only bead at the ceiling;
2 + 3 = 5: they slide over eachother and are replaced by a card.
2 + 4 = 6: the bead jumps on the 2 beads and suddenly realises it is not alllowed to do that, so it jumps to square b;
3 + 3 = 6: very simular “logic” as 2 + 2; 2 2-beads-combinations meet on the same location and result in 1 bead 1 level higher (every column has 4 levels);
3 + 4 = 7: very simular “logic” as 1 + 2; the single bead pushes the 2-beads-combination 1 level higher.