As Boris Johnson arrived in Luxembourg today to meet Jean-Claude Juncker for further Brexit talks, the prime minister and his negotiators were professing growing optimism about the prospects for a last-minute deal.

The European side - including the European Commission president - is much more cautious, noting the immense political challenges facing Johnson.

These lie not just in Brussels - where talks about the Irish border are still a long way from resolution - but also in Westminster where his majority has collapsed and MPs have boxed him in with legislation forcing him to seek an extension if no deal

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The Johnson dream: 'Slice n dice' the Irish backstop

The Northern Ireland-only backstop

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Go back to kicking the can?

The extended transition, sleight-of-hand deal

Conclusion