“We can turn this around in one term.”

So said the new Conservative leader, Kemi Badenoch, to staff at Conservative Campaign Headquarters – in other words, she can win the next general election.

Psychologically, she has to say that and she has to believe it, for why else would someone take on the job of Leader of the Opposition?

Granted, candidates for leader run when they think it is their time – the opportunity may never come around again – but they also have to believe the often thankless slog of opposition is worth it, because turfing out the government is possible.

The arithmetic of doing so – recovering from the Conservatives’ worst ever election defeat and overturning a Himalayan Labour majority – looks a tall order, but so volatile is the electorate you never know.

And so, next for Badenoch, the business of making senior appointments.

Reshuffles are always something of a nightmare for leaders as they are guaranteed deliverers of disappointment and deflated egos as well as sources of smiles and preferment.

But three factors make this one particularly tricky for the new Tory leader.

Firstly, numbers.

There are only 121 Conservative MPs and almost as many shadow ministerial roles to fill, if she wants to man-mark every single minister in government with their own shadow.

One potential solution to this is to ask some junior shadow ministers to shadow more than one brief, but that involves asking them to take on even more work.

And the number is not really 121 because there are those MPs who have said they want to be backbenchers, such as former leader Rishi Sunak, former deputy leader Sir Oliver Dowden, former Chancellor Jeremy Hunt and former Home Secretary and leadership contender James Cleverly for a start.

Then there are those who are chairing select committees and so cannot serve on their party’s frontbench.

And then there are those the leadership would not want to appoint in a million years.

Suddenly, the numbers are getting tight and that is before you offer someone a job and they turn it down and so, implicitly at least, threaten not to serve at all – and that has happened too.

Secondly, the power of patronage.

When you are prime minister, you can pick up the phone and offer real power.

Doing stuff, taking decisions, being in government.

When you are leader of the opposition, you pick up the phone and offer the worthy, democratically vital but ultimately much less appealing role of being a shadow minister.

And thirdly, there is Kemi Badenoch’s authority over her parliamentary party.

She was the first choice for leader of just 35% of Conservative MPs and 57% of party members who voted in the leadership race.

A win is a win, but neither endorsement was emphatic.

All three of these factors swirl as she picks her top team.

What to do with the guy who came second is a perennial challenge for new leaders.

In this instance, what to offer Robert Jenrick and what might he accept?

Word reaches me that there was quite the back-and-forth between Badenoch and Jenrick.

He was offered shadow health secretary, shadow housing secretary, shadow work and pensions secretary, and shadow justice secretary, I am told.

He was not offered shadow foreign secretary.

For a little while on Monday, he did not say yes to any of the jobs he was offered, stewing over whether they were appealing, senior enough or might box him in too much politically.

One Tory source, not close to the leadership, told me: “Kemi just doesn’t like Rob. She thinks his whole schtick about her and whether she has any policies has done her lasting damage with the Right and with Reform voters. This is only likely to further unravel.”

Half an hour or so later, those around Jenrick made it known he had accepted becoming shadow justice secretary, that “the party needs to come together” and that “unity could not be more important”.

But they are not exactly a nest of birds singing in perfect harmony.

Perhaps the biggest appointment of all is shadow chancellor, particularly in the aftermath of a budget that has done much to define how Labour appears to want to approach its early years in office.

Mel Stride is a former cabinet minister, a former minister in the Treasury and a former chairman of the Treasury Select Committee, so it is a brief he is familiar with.

And then there is the decision to make Dame Priti Patel the shadow foreign secretary.

Dame Priti is a long-standing and pretty well-known senior Conservative who has served in government at the highest level as home secretary.

But she is also someone who found herself prematurely out of government back in 2017 after it emerged, extraordinarily, that she had run a freelance foreign policy operation while on holiday in Israel.

Baroness May, who was then prime minister, was furious and Dame Priti resigned before she was fired.

One senior Conservative got in touch with me to claim that Badenoch, in appointing Patel, had “destroyed within 48 hours any chance she had of having a respectable foreign policy”.

Ouch.

No one said opposition was easy.

And these are just the criticisms from Badenoch’s own side.