DOLLAR COMPANY.WORK 91 / A LITTLE MORE TO CARRY
SURELY THERE’S ROOM FOR ONE MORE.
One more
grain.
Four is enough to move things along.
Choose where to begin.
A small field. An open edge.
5 × 5 / ONE GRAIN AT A TIME| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | |||||
| 2 | |||||
| 3 | |||||
| 4 | |||||
| 5 |
A cell with four or more can pass four on: one up, right, down and left. Missing neighbours are beyond the open edge; their grains leave the field.
YOUR CHOSEN CELL
C3 3 grains
Settled. Every cell has fewer than four grains.
Carry out every remaining legal pass in one batch. The pass counter includes all of them.
- Supplied
- 75
- Still on the field
- 75
- Escaped at the edge
- 0
- Passes so far
- 0
75 supplied = 75 on the field + 0 escaped
Three grains in every cell. Add one in the middle and see what needs to move.
Try the same beginning.
Hold this exact field before trying a legal order. Returning restores its grains, full ledger and chosen cell; it clears the last-pass highlight without settling the field.
No beginning held yet. Hold any current field, including one that still has legal passes.
One beginning stays for this visit, even through a new empty or refilled field. Hold again to replace it. It is not included in the static SVG and is lost on reload.
Begin a new field.
These reset the supplied, escaped and pass counters. Your chosen cell stays selected.
The SVG is a static picture of this field, its current status and ledger. You can keep a field that still has passes to make.
Where the passes went.
Each number counts how many times that cell passed four on since this field began. These are passes, not the grains currently in a cell. Adding grains keeps these counts.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 |
| 3 | 0 | 0 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 | 0 |
| 5 | 0 | 0 | 0 | 0 | 0 |
C3 has made 0 passes since this field began.
0 cell passes in total, matching the field’s 0 passes.
New empty and refilled fields start these counters at zero. A held beginning carries its existing counts; Return restores them, including passes made before it was held.
The file is a static count map of the current field. Keep one before returning to a held beginning if you want both pictures.
Try the same beginning, another way.
Start with three in every cell and add one in the middle. Hold this beginning, then choose which ready cell passes next. Return to the beginning and try another legal order. After the same additions and every remaining legal pass, the final field is the same. The intermediate pictures can differ.
This is the classic Abelian sandpile on a fixed field: mathematical grains, not physical sand. Read about the model — Cornell lecture notes (PDF) ↗