Upped docs...

2 files changed, 212 insertions, 11 deletions

diff --git a/challenge-122/james-smith/README.md b/challenge-122/james-smith/README.md
index ae3f9a6cab..a103e128a7 100644
--- a/challenge-122/james-smith/README.md
+++ b/challenge-122/james-smith/README.md
@@ -108,18 +108,218 @@ simple tweak. This corresponds to an approximate reduction of 6.2 in function ca
 By comparing timings on the 2G test machine we note that up to a score of 26 the caching solution is efficient [basically everything in memory] but
 after this streaming solution is the only real option. The difference in time up to this point though is not that great. After we get past 27 the caching algorithm non-longer executes.
 
-| `n` | calls cache | memory cache | time cache | calls stream | memory stream | time stream |
+| `n` | ways | calls cache | memory cache | time cache | calls stream | memory stream | time stream |
 | --: | --: | --: | --: | --: | --: | --: |
-|  5 | 7 | 9,208 | 0.010623 | 7 | 9,196 | 0.010567 |
-| 10 | 22 | 9,204 | 0.010413 | 157 | 9,096 | 0.010751 |
-| 15 | 37 | 10,488 | 0.015361 | 3,313 | 9,096 | 0.016229 |
-| 20 | 52 | 38,916 | 0.117231 | 69,748 | 9,100 | 0.133544 |
-| 25 | 67 | 645,680 | 2.371066 | 1,468,189 | 9,096 | 2.732431 |
-| 26 | 70 | 1,183,636 | 4.619746 | 2,700,421 | 9,100 | 4.930112 |
-| 27 | 73 | 2,176,060 | 23.422928 | 4,966,849 | 9,200 | 8.957511 |
-| 28 | - | - | - | 9,135,460 | 9,096 | 16.605540 |
-| 29 | - | - | - | 16,802,731 | 9,204 | 31.175462 |
-| 30 | - | - | - | 30,905,041 | 9,200 | 61.526530 |
+|  5 | 13 | 7 | 9,208 | 0.010623 | 7 | 9,196 | 0.010567 |
+| 10 | 274 | 22 | 9,204 | 0.010413 | 157 | 9,096 | 0.010751 |
+| 15 | 5,768 | 37 | 10,488 | 0.015361 | 3,313 | 9,096 | 0.016229 |
+| 20 | 121,415 | 52 | 38,916 | 0.117231 | 69,748 | 9,100 | 0.133544 |
+| 25 | 2,555,755 | 67 | 645,680 | 2.371066 | 1,468,189 | 9,096 | 2.732431 |
+| 26 | 4,700,770 | 70 | 1,183,636 | 4.619746 | 2,700,421 | 9,100 | 4.930112 |
+| 27 | 8,646,064 | 73 | 2,176,060 | 23.422928 | 4,966,849 | 9,200 | 8.957511 |
+| 28 | 15,902,591 | - | - | - | 9,135,460 | 9,096 | 16.605540 |
+| 29 | 29,459,425 | - | - | - | 16,802,731 | 9,204 | 31.175462 |
+| 30 | 53,798,080 | - | - | - | 30,905,041 | 9,200 | 61.526530 |
+| 35 | 1,132,436,852 | - | - | - | 650,543,809 | 9,200 | 1,203.608434 |
+| 40 | 23,837,527,729 | - | - | - | 13,693,793,230 | 9,200 | 24,979.923176
+ |
+
+## Number of solutions...
+
+As we have the relationship that if `T(n)` is the number of score combinations for a total of `n` we have:
 
+```
+  T(n) = T(n-1) + T(n-2) + T(n-3)
+```
 
+We see that the sequence of numbers is the *Tribonacci* sequence. Listed
+below to 186 - the highest score in NBA history about ten-quindecillion (10^49) ways to get to that score.
 
+```
+1       1
+2       2
+3       4
+4       7
+5       13
+6       24
+7       44
+8       81
+9       149
+10      274
+11      504
+12      927
+13      1,705
+14      3,136
+15      5,768
+16      10,609
+17      19,513
+18      35,890
+19      66,012
+20      121,415
+21      223,317
+22      410,744
+23      755,476
+24      1,389,537
+25      2,555,757
+26      4,700,770
+27      8,646,064
+28      15,902,591
+29      29,249,425
+30      53,798,080
+31      98,950,096
+32      181,997,601
+33      334,745,777
+34      615,693,474
+35      1,132,436,852
+36      2,082,876,103
+37      3,831,006,429
+38      7,046,319,384
+39      12,960,201,916
+40      23,837,527,729
+41      43,844,049,029
+42      80,641,778,674
+43      148,323,355,432
+44      272,809,183,135
+45      501,774,317,241
+46      922,906,855,808
+47      1,697,490,356,184
+48      3,122,171,529,233
+49      5,742,568,741,225
+50      10,562,230,626,642
+51      19,426,970,897,100
+52      35,731,770,264,967
+53      65,720,971,788,709
+54      120,879,712,950,776
+55      222,332,455,004,452
+56      408,933,139,743,937
+57      752,145,307,699,165
+58      1,383,410,902,447,554
+59      2,544,489,349,890,656
+60      4,680,045,560,037,375
+61      8,607,945,812,375,585
+62      15,832,480,722,303,616
+63      29,120,472,094,716,576
+64      53,560,898,629,395,777
+65      98,513,851,446,415,969
+66      181,195,222,170,528,322
+67      333,269,972,246,340,068
+68      612,979,045,863,284,359
+69      1,127,444,240,280,152,749
+70      2,073,693,258,389,777,176
+71      3,814,116,544,533,214,284
+72      7,015,254,043,203,144,209
+73      12,903,063,846,126,135,669
+74      23,732,434,433,862,494,162
+75      43,650,752,323,191,774,040
+76      80,286,250,603,180,403,871
+77      147,669,437,360,234,672,073
+78      271,606,440,286,606,849,984
+79      499,562,128,250,021,925,928
+80      918,838,005,896,863,447,985
+81      1,690,006,574,433,492,223,897
+82      3,108,406,708,580,377,597,810
+83      5,717,251,288,910,733,269,692
+84      10,515,664,571,924,603,091,399
+85      19,341,322,569,415,713,958,901
+86      35,574,238,430,251,050,319,992
+87      65,431,225,571,591,367,370,292
+88      120,346,786,571,258,131,649,185
+89      221,352,250,573,100,549,339,469
+90      407,130,262,715,950,048,358,946
+91      748,829,299,860,308,729,347,600
+92      1,377,311,813,149,359,327,046,015
+93      2,533,271,375,725,618,104,752,561
+94      4,659,412,488,735,286,161,146,176
+95      8,569,995,677,610,263,592,944,752
+96      15,762,679,542,071,167,858,843,489
+97      28,992,087,708,416,717,612,934,417
+98      53,324,762,928,098,149,064,722,658
+99      98,079,530,178,586,034,536,500,564
+100     180,396,380,815,100,901,214,157,639
+101     331,800,673,921,785,084,815,380,861
+102     610,276,584,915,472,020,566,039,064
+103     1,122,473,639,652,358,006,595,577,564
+104     2,064,550,898,489,615,111,976,997,489
+105     3,797,301,123,057,445,139,138,614,117
+106     6,984,325,661,199,418,257,711,189,170
+107     12,846,177,682,746,478,508,826,800,776
+108     23,627,804,467,003,341,905,676,604,063
+109     43,458,307,810,949,238,672,214,594,009
+110     79,932,289,960,699,059,086,717,998,848
+111     147,018,402,238,651,639,664,609,196,920
+112     270,409,000,010,299,937,423,541,789,777
+113     497,359,692,209,650,636,174,868,985,545
+114     914,787,094,458,602,213,263,019,972,242
+115     1,682,555,786,678,552,786,861,430,747,564
+116     3,094,702,573,346,805,636,299,319,705,351
+117     5,692,045,454,483,960,636,423,770,425,157
+118     10,469,303,814,509,319,059,584,520,878,072
+119     19,256,051,842,340,085,332,307,611,008,580
+120     35,417,401,111,333,365,028,315,902,311,809
+121     65,142,756,768,182,769,420,208,034,198,461
+122     119,816,209,721,856,219,780,831,547,518,850
+123     220,376,367,601,372,354,229,355,484,029,120
+124     405,335,334,091,411,343,430,395,065,746,431
+125     745,527,911,414,639,917,440,582,097,294,401
+126     1,371,239,613,107,423,615,100,332,647,069,952
+127     2,522,102,858,613,474,875,971,309,810,110,784
+128     4,638,870,383,135,538,408,512,224,554,475,137
+129     8,532,212,854,856,436,899,583,867,011,655,873
+130     15,693,186,096,605,450,184,067,401,376,241,794
+131     28,864,269,334,597,425,492,163,492,942,372,804
+132     53,089,668,286,059,312,575,814,761,330,270,471
+133     97,647,123,717,262,188,252,045,655,648,885,069
+134     179,601,061,337,918,926,320,023,909,921,528,344
+135     330,337,853,341,240,427,147,884,326,900,683,884
+136     607,586,038,396,421,541,719,953,892,471,097,297
+137     1,117,524,953,075,580,895,187,862,129,293,309,525
+138     2,055,448,844,813,242,864,055,700,348,665,090,706
+139     3,780,559,836,285,245,300,963,516,370,429,497,528
+140     6,953,533,634,174,069,060,207,078,848,387,897,759
+141     12,789,542,315,272,557,225,226,295,567,482,485,993
+142     23,523,635,785,731,871,586,396,890,786,299,881,280
+143     43,266,711,735,178,497,871,830,265,202,170,265,032
+144     79,579,889,836,182,926,683,453,451,555,952,632,305
+145     146,370,237,357,093,296,141,680,607,544,422,778,617
+146     269,216,838,928,454,720,696,964,324,302,545,675,954
+147     495,166,966,121,730,943,522,098,383,402,921,086,876
+148     910,754,042,407,278,960,360,743,315,249,889,541,447
+149     1,675,137,847,457,464,624,579,806,022,955,356,304,277
+150     3,081,058,855,986,474,528,462,647,721,608,166,932,600
+151     5,666,950,745,851,218,113,403,197,059,813,412,778,324
+152     10,423,147,449,295,157,266,445,650,804,376,936,015,201
+153     19,171,157,051,132,849,908,311,495,585,798,515,726,125
+154     35,261,255,246,279,225,288,160,343,449,988,864,519,650
+155     64,855,559,746,707,232,462,917,489,840,164,316,260,976
+156     119,287,972,044,119,307,659,389,328,875,951,696,506,751
+157     219,404,787,037,105,765,410,467,162,166,104,877,287,377
+158     403,548,318,827,932,305,532,773,980,882,220,890,055,104
+159     742,241,077,909,157,378,602,630,471,924,277,463,849,232
+160     1,365,194,183,774,195,449,545,871,614,972,603,231,191,713
+161     2,510,983,580,511,285,133,681,276,067,779,101,585,096,049
+162     4,618,418,842,194,637,961,829,778,154,675,982,280,136,994
+163     8,494,596,606,480,118,545,056,925,837,427,687,096,424,756
+164     15,623,999,029,186,041,640,567,980,059,882,770,961,657,799
+165     28,737,014,477,860,798,147,454,684,051,986,440,338,219,549
+166     52,855,610,113,526,958,333,079,589,949,296,898,396,302,104
+167     97,216,623,620,573,798,121,102,254,061,166,109,696,179,452
+168     178,809,248,211,961,554,601,636,528,062,449,448,430,701,105
+169     328,881,481,946,062,311,055,818,372,072,912,456,523,182,661
+170     604,907,353,778,597,663,778,557,154,196,528,014,650,063,218
+171     1,112,598,083,936,621,529,436,012,054,331,889,919,603,946,984
+172     2,046,386,919,661,281,504,270,387,580,601,330,390,777,192,863
+173     3,763,892,357,376,500,697,484,956,789,129,748,325,031,203,065
+174     6,922,877,360,974,403,731,191,356,424,062,968,635,412,342,912
+175     12,733,156,638,012,185,932,946,700,793,794,047,351,220,738,840
+176     23,419,926,356,363,090,361,623,014,006,986,764,311,664,284,817
+177     43,075,960,355,349,680,025,761,071,224,843,780,298,297,366,569
+178     79,229,043,349,724,956,320,330,786,025,624,591,961,182,390,226
+179     145,724,930,061,437,726,707,714,871,257,455,136,571,144,041,612
+180     268,029,933,766,512,363,053,806,728,507,923,508,830,623,798,407
+181     492,983,907,177,675,046,081,852,385,791,003,237,362,950,230,245
+182     906,738,771,005,625,135,843,373,985,556,381,882,764,718,070,264
+183     1,667,752,611,949,812,544,979,033,099,855,308,628,958,292,098,916
+184     3,067,475,290,133,112,726,904,259,471,202,693,749,085,960,399,425
+185     5,641,966,673,088,550,407,726,666,556,614,384,260,808,970,568,605
+186     10,377,194,575,171,475,679,609,959,127,672,386,638,853,223,066,946
+```
\ No newline at end of file
diff --git a/challenge-122/james-smith/perl/ch-1.pl b/challenge-122/james-smith/perl/ch-1.pl
index e85a90e949..80be49636d 100644
--- a/challenge-122/james-smith/perl/ch-1.pl
+++ b/challenge-122/james-smith/perl/ch-1.pl
@@ -9,6 +9,7 @@ use Benchmark qw(cmpthese timethis);
 use Data::Dumper qw(Dumper);
 
 stream( map {$_*10} 1..50 );           ## Push values into stream...
+
 eval {say stream_average();} until $@; ## Use eval/$@ to repeat until stream dies.
 
 sub stream {