IT WAS with trademark braggadocio that Donald Trump told the Financial Times, just days before meeting his Chinese counterpart, Xi Jinping, that if China failed to “solve” the problem of North Korea’s nuclear programme, it was “totally” possible that America would do so alone. “China will either help us with North Korea, or they won’t,” said Mr Trump. “If they do, that will be very good for China, and if they don’t, it won’t be very good for anyone.” Mr Trump’s remarks came after the conclusion of a White House review of all the options available for dealing with what Barack Obama had warned would be the most urgent threat to national security under the new administration.

The review, led by Mr Trump’s national security adviser, H.R. McMaster, has looked at everything from pre-emptive military action at one end of the scale to a continuation of Mr Obama’s policy of “strategic patience”. The latter amounted to some discreet disruption of North Korea’s missile launches through cyber-attacks and gentle cajoling of the Chinese to be a bit tougher over the implementation of various UN sanctions. Mr Obama does not claim to have had much success in changing North Korea’s behaviour. Victor Cha, a former American official now at the Centre for Strategic and International Studies, once dubbed it “the land of lousy options”. It remains so.

The most recent addition to the UN’s sanctions was agreed on in November, two months after North Korea’s fifth nuclear test, its second of 2016. China has enforced them by restricting coal imports from its troublesome neighbour this year. As well as the nuclear tests, North Korea conducted 24 missile tests last year, including one successfully launched from a submarine. The tempo of testing has been maintained this year, with the latest launch on April 4th. Preparations also appear to be under way for a sixth nuclear test. Other demonstrations have suggested rapid progress in mastering important technologies, such as solid-fuel rocket motors (allowing quick launches); miniaturisation of warheads (to fit on top of a missile); and re-entry vehicles (to protect a warhead as it plummets through the earth’s atmosphere).

How do you solve a problem like Korea?

North Korea already has missiles that can hit targets anywhere in South Korea or Japan. Soon it will also be able to reach the big American base on Guam. Kim Jong Un, North Korea’s dictator, claimed in his new year address to be in the “final stages” of preparation for a test launch of an intercontinental ballistic missile (ICBM). John Schilling, a missile expert who writes for the website 38 North, reckons that with a warhead weighing around 400kg the North’s prototype KN-08 missile may be capable of reaching most of America’s West Coast. Most analysts think that at its present rate of progress, North Korea will have a working ICBM within four years, as well as up to 50 warheads.

On a trip to East Asia last month, Rex Tillerson, America’s new secretary of state, declared that the time for strategic patience was over. In response to Mr Kim’s ICBM boast, Mr Trump boasted back in a tweet: “It won’t happen!” In the past, Mr Trump, who regards himself as a good negotiator, has suggested that he would be happy to eat hamburgers with Mr Kim in the White House, if that was what was needed to get a deal done to curb North Korea’s missile programme. Mr Trump has swung between sabre-rattling and talk of a grand bargain in part because neither is likely to be successful.

The first option is a pre-emptive strike. An attack that targeted nuclear facilities only, assuming that they could all be found, would still leave intact North Korea’s 20,000 conventional rocket launchers, artillery pieces and heavy mortars. North Korea claims to be able to obliterate Seoul, the South Korean capital, with conventional weapons, turning it into a “sea of fire”. That is an exaggeration. Only a part of its formidable arsenal is in range of Seoul, a metropolis with more than 20m inhabitants. But by conservative estimates, about 130,000 people would die in the first two hours of a bombardment, with the fatality rate declining thereafter as batteries malfunctioned or were destroyed.

However, if the attack and North Korea’s response escalated into full-scale war on the peninsula, as would be likely, millions could lose their lives. America would also probably have to provide a large occupation force in the war’s aftermath. This assumes that China would be prepared to sit on its hands while all this was going on, by no means a certainty.

If a different military approach was adopted, in which the plan was to assemble a force sufficiently overwhelming to destroy Mr Kim’s war machine within a few days, the risks might be even greater. North Korea, seeing what was happening, would lash out, perhaps with its nuclear weapons, before the assault was ready to start. Mr Kim will have learned from the first Gulf war the risks of allowing America to attack at a time of its own choosing.

The military option thus has nothing to recommend it as a means of resolving the problem, although it should stay on the table as a deterrent. The regime must know that to use, or even seriously threaten to use, its nuclear weapons would be an act of suicide. But the flipside is that Mr Kim also knows that military threats as a means of forcing him to give up his nuclear weapons programme are largely hollow. He correctly sees the bombs he is building as the best guarantee of the survival of his regime, along with its slave-labour camps and torture chambers.

The heel’s still alive

The same calculation renders the current sanctions ineffective. North Korea has known much greater hardship—hundreds of thousands of people starved to death in the 1990s—and there is no sign of sanctions fomenting enough discontent in elite circles to encourage a palace coup. Indeed, having purged anyone who could threaten his power, Mr Kim looks more secure than ever. (His uncle, for example, was executed with an anti-aircraft gun.)

There are only two other ways of deflecting Mr Kim from his present course. One is to press China to make life so uncomfortable for the regime that it fears for its survival (the likely intention of Mr Trump’s talk of dealing with North Korea alone if necessary). The other is to offer Mr Kim some sort of deal.

Mark Fitzpatrick of the International Institute for Strategic Studies, a think-tank, says that the chances of getting anywhere are low, but “we have to keep the door open for engagement,” if only because it may be the best way of winning Chinese support for tougher measures. South Korea’s probable new president, Moon Jae-in, will also need to show his supporters that the diplomatic track is still alive.

Four more reasons to worry The initial objective, says Mr Fitzpatrick, should be to get Mr Kim to agree to a moratorium on missile testing and a freeze on plutonium and uranium enrichment at known nuclear sites, which could be verified through surveillance by satellites. In return, there might be some relaxation of sanctions. Another possible carrot would be negotiations on a peace treaty to end the Korean war formally. Mr Fitzpatrick argues that a proposal by the Chinese to end joint American-South Korean military exercises should not yet be considered, much less the withdrawal of American forces from the peninsula. But the hope would be that a little bargain, which would put on hold the development of an ICBM or, worse, submarine-launched missiles that would let North Korea retaliate even after an attack on its terrestrial missile launchers, could turn into a grander bargain leading to de-nuclearisation. Jonathan Pollack, a Korea specialist at the Brookings Institution, is sceptical. “What would talks achieve?” he asks. He thinks that all the evidence indicates that Mr Kim is set on his current path and has no interest in entering into negotiations—at least not until North Korea gains recognition as a de facto nuclear power. That leaves only increased pressure from China as a way to raise the costs of the nuclear programme and, with luck, slow it down. What Mr Trump appears to have in mind is demanding that China halt all financial transactions with North Korea. Anthony Ruggiero, a former Treasury official who advised American negotiators the last time there were talks with North Korea in 2005, argues that the new administration should target banks and other firms that help North Korea evade sanctions. Mr Ruggiero believes that America could levy swingeing fines on Chinese banks that facilitate trade with North Korea, just as it punished European banks that helped customers get around sanctions on Cuba, Iran and Sudan. The ultimate threat would be “secondary sanctions” that deny access to the American banking system, making it impossible to handle transactions denominated in dollars. Mr Obama made little use of secondary sanctions, for fear of provoking such ire that he damaged the wider economic and diplomatic relationship between America and China. That may be a prospect that troubles his successor rather less.

But for all Mr Trump’s apparent confidence in unilateral American action, a strategy that enlists China rather than repels it is likely to be more effective. China, after all, still accounts for about 85% of North Korea’s trade with the outside world. It could cause Mr Kim’s regime extraordinary difficulties by shutting off the pipeline that supplies North Korea with oil, albeit with unpredictable and perhaps chaotic consequences. China also hosts many migrant workers from North Korea.

Which is not to say that Mr Xi can bring Mr Kim to heel with a snap of his fingers, as Mr Trump seems to believe. He probably would if he could do so without triggering a collapse of the regime. If some combination of pressure and engagement continues to fail, containment and deterrence are all that is left. Mr Fitzpatrick says there is no reason to suppose that Mr Kim, who appears rational if exceedingly callous and violent, would invite the destruction of his regime by launching a nuclear attack. But accepting North Korea as a nuclear-armed state might drive South Korea to seek its own nuclear weapons, spurring further proliferation across the region. And North Korea is so opaque that the risk of a catastrophic miscalculation is high.