It’s only a month since the EU referendum vote, but in that time it feels like many of the foundations on which stood a generation or two of political certainties have been removed. This feeling may pass, but in a time of near constant flux and rapid change, one of the constants has been the refrain that “Brexit means Brexit”. However, what that means for the UK, never mind for Scotland, is not yet clear.

Prime Minster Theresa May’s first day in the job was spent in Scotland meeting Nicola Sturgeon, Scotland’s First Minister, to discuss the fallout from the UK Brexit vote and to swap perspectives on how the mandate from voters in Scotland to remain in the EU can marry with the mandate from voters across the UK as a whole to leave. But how can Brexit mean Brexit if, in Scotland, Remain means Remain?

One clear option is independence for Scotland. IPPR Scotland has no position on Scotland’s constitutional future; we’re a cross-party, progressive think tank dedicated to Scotland’s issues and we’ll guard that status jealously now and into the future. However, without doubt the EU referendum vote reopens the constitutional question in Scotland. IPPR Scotland stands ready to support the debate on Scotland’s future whether that means in or out of the EU or the UK.

However, it is those across the UK who do not wish to see Scottish independence, or those open to exploring all the options, who will need to come forward with other options. If it is not to be independence that will meet the Remain mandate in Scotland, then what will? It will require passion, energy and dedication from the UK Government, as well as the Scottish Government, to get this right. And it will also require a tailored approach to Brexit across the UK, placing this principle and the interests of Scotland, Northern Ireland and London up at the top of the priorities when undertaking negotiations with our EU partners.

And even with all the passion and right intentions in the world, this will require a great deal of creativity. How can Scotland, and potentially other parts of the UK, retain a relationship with the EU that’s more like full membership than that of a Brexit UK? On freedom of movement, on access to the single market and crucially on the values that underpin the UK’s new relationships with the world, how can Brexit meet the mandate of the UK and Scotland (and Northern Ireland) at the same time?

In effect, how can a Brexit possibly be both a Remain and a Leave? This sounds like a riddle, and in many ways it is.

But there are multiple potential options, ranging from the far-fetched to the tried and tested. There are existing relationships between the EU and – to name just a few – Norway, Switzerland, Liechtenstein or Canada that could form the basis of a Brexit deal. There is the “reverse Greenland”, where parts of existing EU member states could quit the EU, leaving the other constituent parts to carry on with member state status. And of course, there is potential for the EU to reform in such a way that the multiple mandates of the vote could be delivered.

However likely or unlikely these options seem, they need to be explored with equal vigour and rigour by both the UK and Scottish Governments. The latter is certainly giving the impression of being up for exploring all the options, but without a genuine commitment in the rest of the UK, and without significant reform to Britain as a whole, a tailored approach to Brexit will not be deliverable. And with that, Scotland’s options would be narrowed significantly.

So how can Brexit mean Leave and Remain all at the same time? We will see if this is possible or not. However, one of the only things we can be sure of at this stage is that the UK – including Scotland or not – will need to change fundamentally, or it will be forced to, in order to meet the multiple mandates delivered by the EU referendum result.