No. of Arrangements of token numbers in boxes

  No. of Arrangements in No. of Arrangements in
No. as sum of tokens 3 boxes-15 tokens 3 boxes- 16 tokens 4 boxes- 15 tokens 4 boxes -16 tokens  
6 01 01      
7 01 01      
8 02 02      
9 03 03      
10 04 04 01 01  
11 05 05 01 01  
12 07 07 02 02  
13 08 08 03 03  
14 10 10 05 05  
15 12 12 05 05  
16 14 14 08 08  
17 16 16 11 11  
18 19 19 16 16  
19 20 21 18 18  
20 22 23 23 23  
21 23 25 26 26  
22 24 26 33 34  
23 24 27 37 38  
24 25 28 42 44  
25 24 28 47 49  
26 24 28 52 56  
27 23 28 58 63  
28 22 27 61 68  
29 20 26 64 72  
30 19 25 67 77  
31 16 23 68 80  
32 14 21 69 83  
33 12 19 68 84  
34 10 16 67 86  
35 08 14 64 84  
36 07 12 61 83  
37 05 10 58 80  
38 04 08 52 77  
39 03 07 47 72  
40 02 05 42 68  
41 01 04 37 63  
42 01 03 33 56  
43   02 26 49  
44   01 23 44  
45   01 18 38  
46     16 34  
47     11 26  
48     08 23  
49     05 18  
50     05 16  
51     03 11  
52     02 08  
53     01 05  
54     01 05  
55       03  
56       02  
57       01  
58       01  
  455 560 1365 1820  
      * In case of 4 boxes, if total no. of arrangement is even, max. no. of

 arrangement is even & if total no. of arrangement is odd, max. no. of

 arrangement is odd.

* If no. of tokens is represented by n, no. of sum up to which no. of arrangements are identical to both n and n-1 are

a. n+5 if n is even

b. n+6 if n is odd.

Thus between 16 & 15 tokens identical no. of  arrangements are up to 16+5=21