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 area. n+5 if n is evenb. n+6 if n is odd.Thus between 16 & 15 tokens identical no. of  arrangements are up to 16+5=21