In the game of Jenga, competitors build a tower of identical wooden bricks, creating a new layer each time by deftly removing one block from below and placing it delicately on top.

The higher the tower rises, the more unstable it becomes, and the more skill is required to extract each new brick without bringing the whole structure down.

This aptly describes Theresa May’s Brexit strategy. Salzburg may well prove to be the clumsily extricated brick.

Since the Chequers paper was published in July, both London and Brussels have engaged in a dubious pretence. Theresa May pretended Chequers would allow the UK to maintain frictionless trade with Europe, avoid a hard border in Ireland, and permit free trade deals around the world.

The EU pretended that Chequers might work - or at least, officials and leaders were careful not to slap it down immediately or completely.

It’s important to remember the context of the Chequers publication. In July, Theresa May was barely surviving week-to-week; Tory hardliners were circling; her foreign secretary and Brexit secretary resigned along with a handful of junior ministers; the government was forced into voting for a slew of amendments which contradicted its own strategy.

Theresa May's cabinet at the Chequers meeting in July

One of those amendments rendered the Irish backstop virtually illegal.

The EU looked on helplessly. Member states even decided to suppress a set of European Commission Task Force slides that spelled out in stark detail the cost to the EU over time of allowing the UK to go its own way on services, yet stay aligned to the single market for goods and agriculture - one of the planks of Chequers.

This was done expressly to give Mrs May a helping hand. She barely clung on till the summer recess, but there was a hope that after the summer break, fresher minds might prevail as we headed to the autumn showdown.

But summer came and went and the Tory dynamic was back with a vengeance. Local conservative associations were up in arms over Chequers. Boris Johnson was throwing down weekly gauntlets as his stock among the grassroots rose.

By late August, the British press was convinced that Salzburg would be a pivotal moment. Theresa May would appeal to EU leaders over the head of the doctrinaire Michel Barnier and they would change the chief negotiator’s mandate to give her a deal on the backstop and Chequers.

British diplomats worked the capitals, attempting to peel member states away from the Task Force. Briefing against Ireland’s position on the backstop continued.

All this was viewed with bafflement in Brussels. Downing Street was also worried that that expectations were being unduly raised.

Salzburg was the first time the EU27 would meet Theresa May since Chequers was published. Officials close to the negotiations predicted leaders would carefully calibrate their position. They didn’t want to kill Chequers, but they wanted also to deliver unambiguous support for Ireland.

By Thursday afternoon, the entire charade appeared to have been blown to smithereens.

At a news conference Donald Tusk, the European Council president, seemed to tire of the pretence. He said: "We should not hide the obvious truth. [The Chequers plan] will not work... There are positive elements in the Chequers proposal but the suggested framework for economic co-operation will not work, not least because it risks undermining the single market."

The French President Emmanuel Macron also dismissed the economic parts of the Chequers proposal, and then sharpened the knife with an ad hominem attack on Brexiteers. "Brexit is the choice of the British people... pushed by those who predicted easy solutions... Those people are liars," he said.

In London there was a cascade of negative headlines: "humiliation", "catastrophe", "ambush", "fury". The Sun newspaper, which has denounced Chequers relentlessly from the start, decided that any criticism from EU leaders made them mobsters, under the banner headline "EU Dirty Rats".

Downing Street officials were stunned at Mr Tusk’s intervention. London wondered if this was a deliberate, if high-risk, "Darkest Hour" strategy by which, in a nod to the recent Churchill film, Britain would have to be forced into a crucible of torment in order to finally do a deal.

Some sources wondered was it a miscalculation, or an accidental ramping up of rhetoric. But President Tusk had also tightened the deadline for a deal on the backstop. Unless there was significant progress by the October summit then he would not call a summit in mid-November.

That seemed a harbinger to no deal.

In contrast to the fear and loathing in London, there was thinly disguised amazement in Brussels at the British reaction.

"We never said Salzburg would be a game changer," says one EU diplomat. "That we would dump our line on the backstop, or that we would suddenly think the economic part of Chequers was workable.

"We never hinted at that at any moment."

So what happened in Salzburg? Who tugged at the wrong wooden brick?

Sources suggest that Theresa May got off to a bad start. The Prime Minister was to make her pitch on Chequers and the backstop at a dinner in the Felsenreitschule Amphitheatre the night before the summit.

However, EU leaders were dismayed at what they saw as an aggressive tone, presaged in her article in the German newspaper Die Welt.

Her message was: 'we've moved, now you have to move too'. And she flatly rejected Michel Barnier’s efforts to "de-dramatise" any checks along the Irish Sea by reducing physical checks at GB ports to just one category of goods, with technology and pre-clearance handling the remainder.

"It’s not that she was turning up as a leader," observes one source, "saying to her colleagues, ‘look, I have a major political hurdle here. We all want a deal, but I have a couple of difficulties, can we find common ground on certain issues that are of high concern?'

"That was not the message. The message was, I moved, that was Chequers, that's it. And I cannot accept a border on the Irish Sea."

"That is not very conducive to getting people to say: 'perhaps we should reflect on how we could get further here'."

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Yet, the following morning the Commission President Jean-Claude Juncker described her presentation to reporters at the Mozart University: "It was interesting, it was polite, it was not aggressive. She is doing her job."

As Mr Juncker was speaking Theresa May and Leo Varadkar were holding a bilateral meeting with teams of officials and diplomats at the Sheraton Grand Hotel five minutes walk away.

An Irish source described it as a "useful" meeting, involving an "open exchange of views". Another source present described the encounter as "warm".

Dublin felt that London had to get deeper into the detail of how the backstop would work - how it would be legally operable and all-weather.

Mrs May told Mr Varadkar that she didn't think she could reach agreement on the backstop before the October European Council meeting. She said she would bring forward new proposals shortly to try to break the deadlock.

In Dublin, Simon Coveney was meeting David Lidington, the deputy prime minister. It was, according to London, a "sensible" meeting. There was no inkling of what was about to happen in Salzburg.

Meanwhile, other leaders were arriving at the summit.

Most said the UK needed to move on the backstop, but acknowledged that Chequers had some merit. During the Article 50 gathering, when leaders met without Theresa May, Michel Barnier outlined in detail his reworked plans for the backstop, but he also praised Chequers.

"On Chequers he was extremely nuanced," says one EU source. "He said there are many areas of convergence on which we can work and where we can find common ground. But, he said, the hard [economic] core of it is not workable.

"It was very comprehensible. People had no reason to think we should depart from this approach."

But does that explain the yawning chasm in perception, with "catastrophe" at the British end of the spectrum, and "what-did-she-expect" at the other end?

Diplomats from more than one EU member state insist there was no pre-meditated ambush.

EU officials had clearly indicated in advance of Salzburg that Mr Tusk would work up three themes: a declaration of unity, support for Ireland, and a look ahead to work on the political declaration on the future relationship that will accompany the Withdrawal Agreement.

The issue of timing also came up. While there had been rampant speculation that the deadline for a deal was shifting to mid-November, France in particular was pushing for October.

"There was a view, certainly among the French," says one EU diplomat, "that we should big up October, because if we big up November, then you just make a rod for your own back down the road, because suddenly the EU gets put under pressure."

That, of course, would mean Ireland also coming under pressure.

According to another source, this was the main point of discussion between Donald Tusk and Theresa May when they held a short meeting after the Article 50 lunch.

British sources described the encounter as "frank". There were reports Mrs May left angry and unsettled. An EU source described the meeting as "sociable".

"It was a short meeting," said the source. "They were extremely surprised by the emphasis that was now being placed on October, but that was the dynamic in the room. That was not an ambush."

It is hard not to avoid the conclusion, therefore, that Salzburg was another example, of which there have been many, of a florid mismatch in expectation and perception on either side of the Channel.

This was exacerbated by familiar pattern: an exaggerated expectation within the British system and media about the importance of Salzburg, Theresa May’s posture ahead of it, and the attempts to bypass the Task Force and go direct to heads of government.

"The elements coming together are disparate," says one EU diplomat, "but to a large extent the British brought this on themselves. To the extent that Salzburg was being presented as a great liberation of the process from the clammy cold hands of the ideologues of the Commission bureaucrats - that was never going to happen."

It is undeniable that Donald Tusk’s language in his news conference was blunt. But in the post-Chequers period, neither he, nor other EU leaders, or countless officials, have made any secret of the fact that the economic and customs elements of Chequers were deeply problematic.

The problem is that, whether deliberate or not, Mr Tusk’s intervention threw the notoriously short-termist Downing Street machine into defence mode.

With the party conference imminent, there were few options available to Mrs May other than to present herself in her Downing Street statement as tough and angry, doubling down on the ambush narrative, and casting Salzburg in existential and emotive terms.

She accused the EU of showing her a lack of respect. The EU wanted to "break up our country". She seemed to imply the EU wanted her to overturn the referendum result (the EU has never taken that position). She accused President Tusk of not explaining why the Chequers plan would undermine the single market (in fact, Michel Barnier has spoken non-stop about how Chequers would undermine the single market).

The EU was only offering two alternatives: that of a rule-taker under a Norway plus model, or a Canada-style free trade agreement which would necessitate a backstop.

Neither, she said, were acceptable. Yet, the EU has said Britain’s own red lines are the very things that predetermine those outcomes.

But the uncompromising language on the backstop must be a concern. Theresa May has reinforced the constitutional threat idea, and getting down from that position will be difficult. One Dublin source hopes the speech is merely a "play-within-a-play", scripted for purely domestic consumption.

Ironically, the Salzburg "catastrophe" was not primarily about the backstop, and the chemistry with Leo Varadkar was better than it had been.

Dublin now awaits the new proposals on the backstop, which I understand will cover not just regulatory checks - as some have suggested - but the whole gamut of checks that the backstop will give rise to.

Irish officials are, however, suspicious that the new proposals will be a repackaging of the demand for the backstop to be UK-wide.

But the backstop and Chequers are, of course, intimately linked.

One key reason why EU leaders had been careful not to trash Chequers during the summer is that the White Paper posited the UK more closely to the EU’s regulatory and customs orbit than the visions outlined in Theresa May’s Lancaster House speech.

Even if the economic and customs ideas within Chequers were never going to fly, they altered the trajectory of Brexit from Lancaster House, through the Mansion House speech, and on to a landing zone which could be worked towards, not in October or November, but two years down the line.

Eurosceptics realised this, of course, and that is why they hated it so much.

That landing zone was not fully defined, but a closer customs and regulatory symbiosis between the UK and EU beckoned. Time could have allowed it to materialise.

For Theresa May it was to provide her with cover in order to reassure unionists that the backstop would not ever be needed, because Chequers would inform the future trade relationship in such a way as to remove the need for customs or regulatory checks either on the land border, or down the Irish Sea.

It would also allow her to reassure the business community that highly valuable supply chains would be protected.

While both sides tacitly understood this formulation, there was a critical difference: the EU regarded Chequers as a pseudo-option, a virtual solution that might help close off the Withdrawal Agreement and then guide everyone into the trade negotiations where, over time, the UK would settle for a softer Brexit.

Theresa May saw it as a literal solution.

In Salzburg the virtual met the literal, and the Jenga tower collapsed.