It’s a challenging brain twister of a puzzle, Brendan Shanahan likes to say, for which you don’t get all the pieces at once to spread out on the table and figure it out.

That’s the case for all 30 NHL clubs, and certainly for the Toronto Maple Leafs, who are juggling what they thought they knew about their team, what they now know, and what’s still unclear about the future as the process of trying to move from pathetic doormat to serious contender moves ahead.

New info comes in all the time. Just in the past week, prized farmhand William Nylander took over the scoring lead of the American Hockey League. Two of the players harvested from Mark Hunter’s first draft last June, third rounder Andrew Nielsen (a defenceman with the Lethbridge Hurricanes) and fifth-round pick Dmytro Timashov (a winger with the Quebec Remparts) became the second and third players from that draft (Mitch Marner was the other) signed to entry-level contracts.

It’s a sign that the Leafs are very encouraged by the performances of Nielsen and Timashov early this season. Look for forward Martins Dzierkals of Rouyn-Noranda (QMJHL) to be the next to sign from what the club is very much hoping was a fruitful draft.

At the same time, any number of players on the current NHL roster have, in the first quarter of the season, forced the organization to think more positively about them than they would have in September. Forward Peter Holland, defenceman Roman Polak and winger Joffrey Lupul might fall into that category.

Meanwhile, the team’s two best players so far have been even bigger surprises.

Goaltender James Reimer wasn’t even the team’s No. 1 puckstopper headed into the season, while centre Nazem Kadri was coming off a team suspension last year and came into the fall still viewed as an enigma — so much so that the team had followed up a two-year “bridge” contract with a one-year commitment last summer.

Reimer, so far, has been spectacular at the same time Jonathan Bernier has faltered, while Kadri has been the team’s best forward — and probably its best player, despite basic statistics (two goals, six assists) that would be considered rather pedestrian.

More advanced metrics would buttress the argument that he has played very, very well, not to mention the fact he’s become one of the best in the league at drawing penalties.

Neither player has a contract beyond this season, which is where the Leafs’ puzzle — and their place within it — gets rather interesting.

Nothing has been decided, and there are no contract talks as of yet with either player or their representative. The Leafs have worked hard to reduce the number of contracts they own below the maximum of 50, and are still very much in the process of making their payroll more sensible.

Currently, their actual payroll is about $82 million, but for practical purposes they sit more than $6.7 million below the salary cap of $71.4 million. That’s just how the NHL’s funny math works.

Let’s start with Kadri. He’s still two years away from unrestricted free agency, and the Leafs can grind him for two more one-year deals if they want. His arbitration rights don’t help him much, although that could change as advanced analytics become more established. He’s already making $4.1 million per season, which was a $1-million raise on the season before. That means he’s likely to become a $5-million player next season.

It’s hard to find comparables. Brayden Schenn of the Philadelphia Flyers was picked two slots ahead of the 25-year-old Kadri, and is also headed for restricted free agency next summer after Philly decided to extend Jakub Voracek (eight years, $66 million) and Sean Couturier (six years, $26 million). Schenn is making $2.5 million.

For the Leafs to buy into Kadri’s UFA years with a multi-year deal, they’d have to look at something like $25 million for four years or upwards of $32 million for five years.

Those would be huge numbers for a previously unreliable player who has, yes, clearly flourished under new head coach Mike Babcock, but is also currently headed for a 30-point season. Moreover, with Nylander and Marner both possibly on the NHL roster next season, Kadri’s situation — he currently plays more than any other Leafs — and place on the team’s depth chart could soon be significantly different.

By this time next year, the club may have added a potential star like Auston Matthews to the mix.

In Kadri’s case, the Leafs have all the control, and in the past two negotiations, they’ve used it. With Reimer, the goaltender theoretically has the control with his impending UFA status, but the nature of the goaltending market might dictate otherwise.

He’ll be 28 by season’s end, having been drafted way back in 2006. He’s finishing off a two-year, $4.6 million deal, his third contract with the Leafs. It looked back in 2013 like he’d nailed down the starting job, but the past two seasons first forced the team to acquire Bernier and then vault him past Reimer as the team’s No. 1 netminder.

Now, the two have flip-flopped again this fall, and despite his penchant for allowing bad goals, Reimer’s overall numbers from the first quarter are excellent.

So what to do with him, and where does he fit in the overall puzzle?

The minor-league goalies are Antoine Bibeau, a former star with the Quebec league Val d’Or Foreurs, and Garret Sparks, who by his own admission started taking his profession and personal fitness much more seriously this season and has enhanced his status in the organization significantly.

But Bibeau and/or Sparks are no more certain to become reliable NHL starters than, frankly, Bernier or Reimer. Bernier’s the only one getting paid at the moment, with the Leafs already unsure if the two-year, $8.3 million contract he signed last summer was a mistake.

If Reimer continues to excel, the Leafs will have to look at offering him a multi-year deal, or he might decide to seek a big payday in the UFA market next summer, where goalies like Cam Talbot and Cam Ward may be competition. Or, the Leafs could make him one of the veteran players they’re likely to move for draft picks or prospects before the March trade deadline.

While Kadri has competition coming in Nylander and Marner, Reimer doesn’t really have to look over his shoulder at anyone. He doesn’t have to wonder if the club might draft a goalie in the top five capable of stepping into the NHL right now. As this season progresses, his unsigned status could become more and more of an issue if none of the other goalies in the organization step forward and demonstrate they could fill the void if he leaves.

So, like Kadri, it will be fascinating to watch how the season progresses for Reimer, and what the team decides to do with him. Or what he decides to do with the organization that has hardly been steady in its affection for him over the years.

These are two major question marks for their rebuilding team, players still young enough that they might be contributors if the club becomes a playoff team in the reasonably near future.

They’re pieces of the developing puzzle that Shanahan and Co. already have, while they await the arrival of others. But both are also pieces whose value is anything but set.