Instead of the 23 players who should be stripped for action in Belfast tonight there will only be 22 because, in spite of a huge increase in their resources this season, they have, quite simply, run out of props.
It is an extraordinary situation, not least because they have nine full-time props on their books, having signed internationalists Ofa Fainga'uku from Tonga and German Araoz from Argentina in the course of the season to supplement an already impressive group.
Araoz was recruited too late to be included in Glasgow's 30-man Heineken Cup squad so, like Jon Welsh and Ed Kalman, the Scottish international pair, who are both coming back at club level for Stirling County tomorrow after long injury absences, he is ineligible.
Meanwhile, three of the six – Mike Cusack, Fainga'uku and Hunter – who are among the 10 front-row forwards that the rules dictate must be named in their squad, all picked up injuries in quick succession and are sidelined.
Consequently, following discussions with the tournament organisers, a club with one of the strongest group of props in Europe has been forced to name a squad that includes the listing "no-one available" at No.18.
Gregor Townsend, their head coach, did admit that, in competitive terms, this could have been worse for Glasgow since this is a competition they are out of, unlike the Pro12 where they lie second in the table. However, he also noted that had it been a Pro12 match, their strength in depth would have properly come into play since the returning players could have been considered.
Given that replacement benches were extended, first to seven players then to eight, to try to ensure that the risk of having to revert to uncontested scrummages could be minimised, it would seem it is time for the administrators to think again.
It should not be too difficult to frame a rule that is specific to front-row forwards and states that those officially on the club books before the Heineken Cup got under way, could be recalled under such circumstances.
Glasgow are also making the trip without back-row cover on the bench because of a similar situation, but on the plus side, the nine men who have produced two impressive pack performances in their last two matches are all available for what is currently one of the most formidable challenges in the European games.
Consequently, Townsend reported that those curious circumstances afflicting their bench have not had a major impact on their preparations. For all that they have contributed to a dismal effort by the Scottish teams in the Heineken Cup at a delicate time for the negotiators trying to protect their places in it, he says they are excited by tonight's challenge. "It's a great game," he said. "We're going into a sell-out stadium, up against one of the best teams in Europe, it's the first game on Sky over the weekend and we're on a good run of form and want to take that into another week.
"You want to measure yourself against the best teams and we know we've got that this week and with Northampton, who are in the top four in England, the following week too.
"There's always great motivation to be announced in the team to play in these big games, so whether we're going to qualify or not, it should have the same level of motivation for our players."
While Ruaridh Jackson, potentially Scotland's playmaker for the RBS 6 Nations Championship, is another who misses this match through injury after damaging ribs last weekend, there is no major concern about his international prospects.
With the new Scotland management having been announced this week, though, his absence does allow one of his main rivals for the role, clubmate Dunc Weir, an opportunity to catch the eye.
On which note Townsend added his backing to those who believe that Rob Harley, Glasgow's perpetual motion flanker, has strengthened his case for further Test honours with his performances at openside flanker, even comparing him with one of the country's greatest back-row forwards.
"He loves tackling, doesn't fade in games, his clearing at rucks is excellent and I think he's enjoyed playing in the position. It means he gets to tackle even more," the coach observed.
"I do think that some players now are making the transition from blindside to openside, such as Chris Robshaw, the England captain, and Tom Wood, if they love the contact area, and Rob excels there.
"Someone described him to me as being a bit like John Jeffrey, and I do see the good parallel there with JJ of getting stuck in and putting the body on the line, but he is a clever rugby player as well. He prepares really well in the lineout, knows his support lines perfectly and you only need to tell Rob something once and he goes out and does it."