
The renumbering happened indeed towards the end of the Quiet revolution, when most of modern governmental institutions were commissioned, driven by the nationalistic policies ― not necessarily separatist or chauvinist, but rather leaning towards republicanism and state-interventionism ― of the ill-named Liberal Party. I do not think the renumbering was purely technical, but I do not think it was either directly ordered by politics. It was just a thing at that time, to shake things over and start anew. This little guy over there was the face of the 1971-1974 renumbering. Though appearing as silly, it is a blatant example of the growing conscience of the Québecois culture at the time. The parallel between Asterix's village in the Roman Empire and Québec's cultural exception in North America is caricatural, and the MTQ most likely deliberately chose to make their operation funny.
Per the 1971-1972 MTQ annual report, the renumbering was implemented to optimize itineraries. The Ministry developed a simple, "easy-to-remember" numbering system. At the time, the great itineraries we know today were cut into bits and pieces; 116, 117, 132 and 138 all had at least different 4 designations versus their actual status, while linking major destinations. There was
some logic to the new grid, but many new numbers inherited loosely from the previous one, still fitting in that grid : 8 became 14
8 (instead of, say,
150), the most frequented leg of 11 mostly became
117 (why not
115?), 13 became
139 (while the neighbouring R-39 was replaced by R-243... that one boggles me), 19A became
15
9, 22 became part of 1
22, 24 became
20
4, 40 became 1
04 and so on. Some itineraries have seen less change in their routing and did not have a logical or inherited number : 29 became 344, 34 became 161, 41 became 158 and 1 was closely followed by R-112
(Sidenote to Route 1: its low number shows how it is intricately linked to the early stagecoach and colonisation routes along Craig/Gosford (Québec-Sherbrooke) and Stagecoach (Montréal-Sherbrooke) roads. Route 2 would have been among the few predecessors to route 1 as a public ― or "royal" ― road, maintained by the colony rather than the seigniors. While not the most frequented today, Route 1 has then been a known itinerary since the early 1800's, in the beginnings of land travel in Canada).
The overall budget for this project was $550,000 and the newly numbered network added 3,600 miles of roads to the existing 7,500 miles of official itineraries.
The first phase happened in 1971-1972. It aimed at identifying previously unnumbered secondary roads (2xx and 3xx). The second phase, that effectively
re-numbered roads was implemented in the Spring of 1973. One year later, the renumbering was 95 % complete. The shields bearing the former numbers still stood up for a while, stroke by a black diagonal line to indicate the decommissioning.
The 1971-1974 renumbering was the second one in 40 years. In the late 20's or early 30's (most probably the latter), the MVQ reviewed their primitive numbering system then again to simplify itineraries. This is when route 2 connected Ontario to New Brunswick, and US-5 and 7 were harmonised with their Québec counterpart. It still wasn't perfect, with numbers 15 and 16 being used to designate pretty much every highway north of the Saint Lawrence, east of Québec City.
1927 map :
https://collections.banq.qc.ca/ark:/52327/22439081933 map :
https://collections.banq.qc.ca/ark:/52327/2827254That first renumbering occurred pretty much concomitantly to the Gordon and Vautrin colonisation plans, which drove tens of thousands of people off the unemployment-plagued cities towards unsettled land, opening new regions that needed... new roads! There was no provision for new, logical highway numbers even after the 1930's renumbering, so this system was rapidly rendered obsolete. Before the 1930's, the hinterland where routes 232, 234, 291 to 298 and 382 to 399 nowadays run, for example, was open forest, devoid of permanent occupation except for aboriginal peoples and logging or mining camps. The inception in 1966 of a province-wide autoroute numbering system formalized duplicate numbers for two different, unrelated roads : route 20 and A-20 were closely parallel, but that was merely an exception to routes 5, 10, 15, 25, 30, 35 and 40, that were tens, nay hundreds of miles away from their autoroute counterpart. That was for sure the final nail in the coffin for the old numbering system.
EDITED to explain better the choice of numbers and better answer the question