Original Kansas numbering

[NE2]

Sources:
http://www.historicalroadmaps.com/KansasPage/1926ClasonsKansasPage/image1.html
http://broermapsonline.org/online/NorthAmerica/UnitedStates/NorthCentral/Kansas/index.html (1926)
http://www.davidrumsey.com/luna/servlet/detail/RUMSEY~8~1~33758~1171474:Rand-McNally-junior-auto-road-map-K (1927 - numbers that are different on this map are shown after an arrow)
http://www.ksdot.org/burtransplan/maps/HistoricStateMaps/1932Mapside.pdf
A list of federal aid routes from 1925 and those added in 1926

It appears that the initial system assigned numbers to the federal aid routes and no others, though there are a few possible violations of this (a few routes probably had gaps). U.S. Routes in the 1925 plan did not receive state numbers. It's not clear if U.S. Route numbers were skipped; there was a 36 to match MO 36, but I can't find 40 or 50.

First came numbers that matched adjacent states:
1: OK (match) - 22 Woodruff?
5: US 166 Galena - NE (match) (-> mostly US 73/73E, except just north of KC)
7: OK (match) - 5 Lansing
8: OK (match) - US 36 Smith Center
14: 44 Anthony - NE (match)
16: OK (match) - US 36 Troy
20 -> 23: 96 Dighton - NE (match, before and after renumbering due to US 20)
22: OK - NE (match)
24 -> 56?: US 71 Pleasanton - MO (24 -> 52) (unsure about this one - may have always been 56, in which case where was 24?)
26: OK (match) - US 81 South Haven (unsure about this one)
36 -> 12: Elkhart - MO (match, before and after renumbering due to US 36)
51: CO (match) - 25 Elkhart (unsure about this one - it was FA in 1923 but not 1926)
57: Junction City - MO (match)
92: 30 McLouth - MO (match)
96: CO (match) - 5 Crestline

Then the remaining major north-south routes got odd numbers in order from east to west:
3: 57 Brazilton - 38? Xenia
9 -> 6: OK (6) - 7 Osawatomie
11: Chautauqua - US 36 Beattie
13: US 77 De Graff - Manhattan
15: US 77 Udall - US 36 Washington (matched NE after extension)
17: US 54 Kingman - US 81 McPherson
19: US 50S Belpre - Larned
21: OK - NE (future match)
23 -> 25: 36 Hugoton - NE (3C -> 25)
25 -> 27: Elkhart - NE

A few east-west routes were given numbers roughly from north to south (exactly if you assume 4 and 10 were numbered to match):
2: CO (102) - 22 Norton
4: 96 Shaffer? - Atchison (may have been numbered to match MO 4, although that ended at St. Joseph in 1926 and only extended to Atchison in 1927, replacing 52)
6 -> 9: 22 Dresden - Atchison
10: 4 Herington - KC (may have been numbered to match MO 10, now 210)
12 -> 24: US 77 Leonardville - 4 Valley Falls
18: US 40N Bogue - US 81 Bennington

But then all even numbers until 28 were already used to match. Beginning with 27, numbers were assigned to shorter routes in a rough clustering pattern from north to south (43 and 48 don't fit for whatever reason):
27 -> 20: 6 Whiting - 16 Troy
28: 14 Jewell - Concordia
29: Manhattan - 11 Wabaunsee
30: 4 Rock Creek - US 40 Tonganoxie
31: 11 Eskridge - US 75 Lyndon?
32: Lawrence - KC
33: US 75 Waverly? - 5 Louisburg?
34 -> 31: US 75 Waverly? - Garnett
35: 7 Beagle - 5 La Cygne
37: Kinsley? - 8 Seward
38: 9 Kincaid - 5 Fulton (unsure about this one)
39: 96 Fredonia - 7 Fort Scott
40: skipped?
41 -> US 54: 36 Meade - US 54 Bucklin
42: 8 Coats - Wichita
43: 4 Hope - US 40S Detroit (doesn't fit the pattern)
44: 8 Kiowa - 16 Coffeeville (-> US 166 east of South Haven)
45: 23 Hugoton - Dodge City
46: CO (118)? - 22 Santa Fe
47: 96 Lafontaine - 16 Morehead (very unsure about this one - there seem to have been some early changes in this area)
48: 7 Mound City - 5 Pleasanton (unsure about this one; doesn't fit the pattern)
49: 44 Corbin? - 36 Mayfield

And then a few more routes got numbers (it's possible that the state didn't take them over until after the others were numbered):
50: skipped?
52: 22 north of Scott City - 1 La Crosse? (not FA in 1926)
53: US 81 - 15 Mulvane
54: skipped?
55: US 81 Belle Plaine - 15 Udall
58: Lenexa - Overland Park (probably had an earlier number)
70: 11 north of Emporia - Reading (probably had an earlier number)

The only FA route I'm sure about that I couldn't find a number for is from 33 east of Ottawa to US 50 Edgerton, which became part of 33 in 1927 (old 33 became 68). Two others are sketchily defined and may have never been state highways or may have been redundant definitions of other routes:
96 directly north to Cherryvale
39 Porterville - US 54 Uniontown

[NE2]

Finally, here's the FA list:

[1925]
The routes embraced in this system are indicated by the following control points:
1. From the Missouri-Kansas line at the west end of the Missouri river bridge opposite St. Joseph, Mo., via Troy, Hiawatha, Fairview, Sabetha, Seneca, Marysville, Hanover, Haddam, Belleville, Mankato, Smith Center, Phillipsburg, Norton, Dresden and Selden, to a point on the federal-aid road between Halford and Colby.
2. From the Kansas-Nebraska line near Reserve, via Hiawatha and Horton, to a point on the federal-aid road between Atchison and Effingham near Lancaster; and from Atchison, via Leavenworth, to a point on the federal-aid road between Kansas City and Tonganoxie.
3. From a point on the federal-aid road between Norton and Dellvale, via Oberlin, Atwood, Wheeler and St. Francis, to the Kansas-Colorado line near Gurney, Colo.
4. From a point on the Kansas-Missouri state line at Kansas City, via Louisburg, Trading Post, Pleasanton, Fort Scott and Pittsburg, to a point on the federal-aid road between Baxter Springs and Galena.
5. From Horton to Whiting.
6. From Atchison, via Nortonville and Oskaloosa, to Williamstown; and from Lawrence to Baldwin City; and from Ottawa, via Garnett, Iola, Chanute, Erie and Parsons, to Altamont; and from Oswego, via Chetopa, to the Kansas-Oklahoma line south of Chetopa.
7. From a point on the federal-aid road between Carbondale and Lyndon three miles east of Scranton, via Scranton, to Burlingame.
8. From Burlington, via Le Roy, to Iola.
9. From Atchison, via Whiting, Netawaka and Frankfort, to Blue Rapids; and from Waterville, via Clifton, to Concordia; and from a point on the federal-aid road between Concordia and Minneapolis to Beloit.
10. From a point on the federal-aid road between Chanute and Shaw near Earleton, via Cherryvale and Coffeyville, to the Kansas-Oklahoma line south of Coffeyville.
11. From Kansas City, via Olathe, Bonita, Baldwin City, Ottawa, Waverly, Emporia, Cottonwood Falls, Florence, Peabody, Newton, Hutchinson, St. John, Kinsley, Dodge City, Cimarron, Garden City, Lakin and Syracuse, to the Kansas-Colorado line near Coolidge.
12. From the Kansas-Nebraska line north of Sabetha to Sabetha; and from Fairview, via Netawaka, Holton and Topeka, to a point on the federal-aid road between Overbrook and Scranton; and from a point on the federal-aid road two miles north of Lyndon, via Lyndon, to a point on the federal-aid road between Waverly and Lebo; and from the same route, via Burlington, Yates Center, Buffalo, Altoona and Independence, to Caney.
13. From Leavenworth to Oskaloosa.
14. From a point on the federal-aid road south of Eskridge, via Burlingame, to Osage City.
15. From a point on the federal-aid road between Nortonville and Oskaloosa, via Valley Falls and Meriden, to a point on the federal-aid road between Hoyt and Topeka.
16. From Bonita, via Paola, Osawatomie and Mound City, to a point on the federal-aid road between Pleasanton and Prescott; and from Fort Scott, via Girard and Columbus, to the Kansas-Oklahoma line near Picher, Okla.
17. From Manhattan to a point on the federal-aid road east of Riley; and from a point on the federal-aid road east of Leonardville, via Leonardville, Clay Center, Glasco, Beloit, Osborne, Stockton, Bogue, Hill City and Hoxie, to Halford.
18. From Frankfort, via Westmoreland, Wamego, Alma, Eskridge, Admire and Emporia, to a point on the federal-aid road between Eureka and Neal; and from Eureka, via Severy, Howard and Moline, to Sedan.
19. From a point on the federal-aid road between Salina and Bennington, via Lincoln, Waldo and Plainville, to Bogue.
20. From the Kansas-Nebraska line north of Marysville, via Marysville, Riley, Junction City, Herington and Marion, to a point on the federal-aid road between Florence and Peabody; and from Florence to El Dorado; and from Augusta, via Winfield and Arkansas City, to the Kansas-Oklahoma line south of Arkansas City.
21. From Kansas City, via Tonganoxie, Lawrence, Big Springs, Topeka and St. Marys, to Wamego; and from a point on the federal-aid road south of Wamega, via Wabaunsee, Manhattan, Junction City, Abilene and Salina, to Ellsworth; and from a point on the federal-aid road between Ellsworth and Lincoln, via Wilson, Russell, Hays, Wakeeney, Grainfield, Oakley, Halford, Colby and Goodland, to the Kansas-Colorado line near Kanorado.
22. From a point on the federal-aid road between Haddam and Hanover north of Washington, via Washington, to a point on the federal-aid road between Linn and Barnes.
23. From Oakley, via Winona, to Sharon Springs.
24. From a point on the federal-aid road east of Clifton, via Morganville, to a point on the federal-aid road west of Clay Center.
25. From Kansas City, via Bonner Springs, Lawrence, Williamstown, Topeka, Dover and Eskridge, to Council Grove.
26. From the Kansas-Nebraska line near Chester, Neb., via Belleville, Concordia, Minneapolis and Salina, to a point on the federal-aid road between Gypsum and Assaria; and from McPherson, via Moundridge, Newton, Wichita, Wellington, South Haven and Caldwell, to the Kansas-Oklahoma line south of Caldwell.
27. From Baldwin City, via Overbrook, Osage City, Admire, Council Grove, Herington, Gypsum, Lindsborg, McPherson, Lyons, Great Bend and Larned, to Kinsley.
28. From a point on the federal-aid road between McPherson and Moundridge east of Inman, via Inman, Medora and Hutchinson, to a point on the federal-aid road between Kingman and Goddard, south from Hutchinson.
29. From Lindsborg, via Marquette and Geneseo, to Hoisington; and from a point on the federal-aid road between Russell and Boyd, to a point on the federal-aid road between Shaffer and Rush Center.
30. From the Kansas-Nebraska line near Superior, Neb., via Mankato and Beloit, to Lincoln; and from a point on the federal-aid road west of Lincoln, via Ellsworth, Lyons and Sterling, to a point on the federal-aid road west of Kingman; and from Kingman, via Harper, to Anthony.
31. From Ottawa, via Quenemo, to a point on the federal-aid road south of Lyndon.
32. From Smith Center, via Osborne, Waldo, Russell, Hoisington, Great Bend, St. John, Pratt, Lake City, Medicine Lodge and Kiowa, to the Kansas-Oklahoma line south of Kiowa.
33. From Great Bend, via Rush Center, Ness City, Dighton, Scott City and Leoti, to Tribune.
34. From the Kansas-Nebraska line north of Phillipsburg, via Phillipsburg, Stockton, Plainville, Hays and La Crosse, to Rush Center; and from Kinsley, via Greensburg and Coldwater, to the Kansas-Oklahoma line near Coy, Okla. [1923: this was split between 34 and 36, and 36-42 were 38-44]
35. From the Missouri-Kansas line east of Trading Post to Trading Post.
36. From Norton, via Hill City, Wakeeney, Ness City and Jetmore, to a point on the federal-aid road between Wright and Dodge City; and from Dodge City to a point on the federal-aid road between Bloom and Minneola.
37. From a point on the federal-aid road between Trading Post and Louisburg three miles east of La Cygne, via La Cygne, to a point on the federal-aid road between Beagle and Cadmus.
38. From Grainfield, via Gove City, to Dighton.
39. From Osawatomie to Garnett.
40. From the Kansas-Nebraska line north of Atwood, via Atwood, to Colby; and from Oakley, via Scott City, Garden City, Santa Fe, Springfield and Liberal, to the Kansas-Oklahoma line south of Liberal.
41. From a point on the federal-aid road between Great Bend and St. John east of Seward, via Seward, Larned and Jetmore, to Garden City.
42. From Russell Springs to a point on the federal-aid road between Winona and Page; and from Leoti, via Lakin and New Ulysses, to Hugoton.
43. From a point on the federal-aid road between Wichita and Goddard, via Andale and Haven, to a point on the federal-aid road south of Hutchinson; and from Hutchinson, via Nickerson, to a point on the federal-aid road south of Sterling.
44. From the Kansas-Nebraska line northwest of St. Francis to St. Francis; and from Wheeler, via Goodland, Sharon Springs, Tribune, Syracuse, Johnson and Richfield, to Elkhart.
45. From the Kansas-Missouri line east of Fort Scott, via Fort Scott, Iola, Yates Center, Eureka, El Dorado, Augusta, Wichita, Goddard, Kingman, Pratt, Greensburg, Bucklin, Minneola, Meade and Plains, to Springfield; and from a point on the federal-aid road between Springfield and Liberal, via Hugoton, to Elkhart.
[1923: 46. From Leoti via Lakin and Ulysses to Hugoton. became part of 42]
47. From a point on the federal-aid road between Bucklin and Mullinsville to Dodge City.
[1923 (last even number): 48. From Kansas-Nebraska line northwest of St. Francis, via St. Francis, Goodland, Sharon Springs, Tribune, Syracuse, Johnson and Richfield, to Elkhart. became 44]
49. From Santa Fe, via New Ulysses, to Johnson.
51. From Girard to a point on the federal-aid road south of Arma; and from Frontenac to a point on the Kansas-Missouri state line near Mindenmines, Mo.
53. From Chanute to an intersection with the federal-aid road between Buffalo and Altoona.
55. From Altoona, via Fredonia, to Severy.
57. From a point on the federal-aid road between Pittsburg and Crestline, via Columbus, Oswego, Altamont, Independence, Moline, Winfield and Wellington, to Harper; and from a point on the federal-aid road between Harper and Anthony to Medicine Lodge; and from Lake City, via Coldwater and Ashland, to intersect the federal-aid road between Minneola and Fowler.
59. From the Kansas-Missouri state line at Galena, via Baxter Springs, Chetopa and Coffeyville, to Caney; and from Havana, via Sedan and Arkansas City, to the federal-aid road north of South Haven.
61. From a point on the federal-aid road between Marion and Aulne to McPherson.
[1923 (last odd number): 63. From the road between Richfield and Elkhart west to the Kansas-Colorado line. did this become anything?]
65. From Cherryvale to the federal-aid road between Independence and Altamont.
66. From Pittsburg, via McCune and Parsons, to Cherryvale.
67. From Fulton, via Mapleton, Xenia, a point west of Xenia, a point west of Blue Mound and Kincaid, to a point on the federal-aid road south of Garnett.
68. From South Haven to the Kansas-Oklahoma state line south of South Haven (en route to Blackwell, Okla.).
69. From Caney to the Kansas-Oklahoma state line south of Caney.
70. From Oskaloosa to a point on the federal-aid road between Valley Falls and Meriden.
71. From Erie to Girard.
72. From Chanute to a point on the federal-aid road between Fort Scott and Girard east of Hiattville.
73. From Downs, via Kirwin and Densmore to Dresden.
74. From Concordia to a point on the federal-aid road between Mankato and Beloit near Jewell.
75. From Rush Center to a point on the federal-aid road west of Larned; and from another point on the same federal-aid road near Rozel to Kinsley.
76. From a point on the federal-aid road between Wichita and Wellington near Belle Plaine to a point on the federal-aid road between Augusta and Winfield east of Udall.
77. From Burlington to a point on the federal-aid road between Waverly and Emporia.
78. From Sharon Springs to the Kansas-Colorado state line en route to Cheyenne Wells, Colo.
79. From Frankfort to a point on the federal-aid road between Seneca and Marysville.
80. From a point on the federal-aid road near Wamego, via St. George, to Manhattan.
81. From a point on the federal-aid road between Herington and Gypsum, via Hope and Enterprise, to a point on the federal-aid road, between Junction City and Abilene.
82. From a point on the federal-aid road between Ashland and Minneola to a point on the federal-aid road near Meade.
83. From a point on the federal-aid road north of Bonner Springs, via Bonner Springs, to Olathe.
84. From a point on the federal-aid road between Fort Scott and Chanute, via Moran, to Kincaid.
85. From a point on the federal-aid road between St. John and Kinsley to Larned.
86. From Cottonwood Falls, via Cassoday, to a point on the federal-aid road near DeGraff.
87. From a point on the federal-aid road west of Fort Scott, via Devon, to Mound City.
88. From a point on the federal-aid road between Kansas City and Olathe to a point on the federal-aid road between the Kansas-Missouri state line and Louisburg.
89. From a point on the federal-aid road between Oskaloosa and Leavenworth to Tonganoxie.
90. From a point on the federal-aid road between Emporia and Admire to Reading.
91. From a point on the federal-aid road between Fort Scott and Chanute to a point on the federal-aid road between Bronson and Uniontown; and from Bronson to a point on the federal-aid road west of Xenia.
92. From a point on the federal-aid road between Mayfield and Milan to Caldwell.
93. From Anthony to a point on the federal-aid road between Caldwell and a point on the federal-aid road between Mayfield and Milan.
94. From a point on the federal-aid road between Wichita and Belle Plaine to Mulvane.
95. From a point on the federal-aid road between Belle Plaine and Udall, via Mulvane and Derby, to Wichita.
96. From a point on the federal-aid road south of Leavenworth, via Wolcott, to a point on the federal-aid road between Kansas City and Bethel.
97. From Louisburg to Ottawa.
98. From a point on the federal-aid road east of Baldwin, via Wellsville, to a point on the federal-aid road between Louisburg and Ottawa.
99. From a point on the federal-aid road north of Garnett, via Harris, to a point on the federal-aid road east of Waverly.
100. From Lawrence, via Eudora, to a point on the federal-aid road west of Zarah; and from Zarah to a point on the federal-aid road between the Kansas-Missouri state line at Kansas City and Louisburg.
101. From a point on the federal-aid road north of Phillipsburg near the Kansas-Nebraska line to a point on the federal-aid road between Norton and Phillipsburg near Calvert.

[1926]
102. From a point on the federal aid road near Valley Falls, via Holton, to a point on the federal aid road north of Westmoreland, and from a point on the federal aid road west of Westmoreland to a point on the federal aid road between Riley and Randolph.
103. From a point on the federal aid road near Clay Center to a point on the federal aid road near Abilene.
104. From Junction City to Dwight.
105. From a point on the federal aid road between Topeka and Eskridge, via Alma and Alta Vista, to Herington.
106. From a point on the federal aid road near Grainfield, via Hoxie, to a point on the federal aid road between Oberlin and Norton.
107. From Wichita, via Clearwater and Rego, to a point on the federal aid road near Coates.
108. From Troy to Atchison and from a point on this road south of Troy to a point on the federal aid road east of Horton.
109. From Fredonia to a point on the federal aid road near Elk City.
110. From a point on the federal aid road north of Cherryvale, near Moorehead, to a point on the federal aid road between Independence and Altoona, and from another point on the same federal aid road between Independence and Altoona, near Neodesha, to a point on the federal aid road between Elk City and Fredonia.
111. From a point on the federal aid road near Severy to a point on the federal aid road near El Dorado and Augusta.
112. From Abilene to a point on the federal aid road near Hillsboro, and from a point on the federal aid road west of Hillsboro to Newton.
113. From Anthony to Kiowa.
114. From a point on the federal aid road between Sedan and Niotaze to Chautauqua.
115. From Manhattan, via Alta Vista and Council Grove, to a point on the federal aid road between Emporia and Strong.
116. From the Kansas-Missouri state line, near Opolis, to a point on the federal aid road between Pittsburg and Crestline.
117. From a point on the federal aid road west of Girard, via Brazilton and Hepler, to Uniontown.
118. From Dodge City, via Haggard, Copeland and Satanta, to a point on the federal aid road between New Ulysses and Hugoton.
119. From a point on the federal aid road between Ashland and Meade to Englewood.
120. From Oberlin to the Kansas-Nebraska state line, en route McCook.

[J N Winkler]

What is the source for these federal-aid numbers?  They don't line up with FAP numbers historically used in Kansas.  E.g. no. 38 in the list corresponds to K-23 between Grainfield and Dighton, while F-038-3(35) is the FAP designation for the US 54 improvement project that includes the Wichita airport connector.

[NE2]

What is the source for these federal-aid numbers?

Kansas Highway Commission biennial reports: http://www.google.com/search?tbm=bks&q=%22The+routes+embraced+in+this+system+are+indicated+by+the+following+control+points%22

[J N Winkler]

Thanks for this--it seems evident, from the context, that the numbering was not intended to match a FAP numbering scheme.

[NE2]

Sure, but I only included that list in case someone wants to replicate the results of the first post.

[route56]

It's not clear if U.S. Route numbers were skipped; there was a 36 to match MO 36, but I can't find 40 or 50.

One of the most important tasks was the designation of a new state highway system. The highway department had begun drawing maps in June [1925] for a tentative network in each county. Through the summer the maps were sent to the boards of counties for study before the county boards and the highway commission worked out a final plan — a tricky business as it turned out. Not only must the total state system incorporate the federal network but it must be limited to 8,690 miles of roadway carefully apportioned among 105 counties. The state mileage in each county could be no less than the sum of the county's north-south and east-west dimensions and must connect its county seat with its principal market centers. Finding connections which satisfied county boards, the highway commission and the Bureau of Public Roads dictated lengthy and delicate negotiations because every shift in routes drew loud complaints from bypassed communities. The various parties forged agreement on the first county maps in October, 1925, but not until September, 1926, were the last ones approved.

Since planning for the Kansas System took place during the same timeframe as the US system, I'm confident that they did indeed skip the numbers 40 and 50.