Balls remaining: 256
Controls
Distribution
Bin 0
0
Bin 1
0
Bin 2
0
Bin 3
0
Bin 4
0
Bin 5
0
Bin 6
0
Bin 7
0
Bin 8
0
Observed
Pascal's row: 1, 8, 28, 56, 70, 56, 28, 8, 1
Pascal's Triangle
1
11
121
1331
14641
15101051
1615201561
172135352171
18285670562881
Row 8 = C(8,k) for k=0..8. Each number counts the paths from top to that bin.
How It Works
Each peg is modeled as two competing Petri net transitions (left/right) sharing one input place. With equal rate constants, mass-action kinetics splits flow equally at each peg.
The bin counts are determined entirely by topology: bin k has C(8,k) paths leading to it. More paths = more flow = higher count. That's the binomial distribution.
45 places (1 entry + 36 peg positions + 8 intermediate + 9 bins), 72 transitions (2 per peg), 256 balls (28).