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UEFA’s convoluted co-efficient process means the final weeks of the season can see clubs pursuing two different routes to European football via both league and cup. This was the case for Hearts 12 months ago, climaxing in a memorable Scottish Cup semi-final win against Hibs at Hampden Park. This year, the matter of guaranteeing a group-stage berth is now out of their hands.

Celtic’s win at Tynecastle Park on Saturday eliminated the Edinburgh club from this season’s cup at the quarter-final stage. Finishing third in the cinch Premiership is now the only objective for manager Robbie Neilson and players. That alone would secure a spot in the Conference League’s third qualifying round. Defeat at that stage would end the European adventure at the first hurdle. The team finishing fourth enters one step earlier at the second qualifying round.

The Scottish Cup winners earn a much more rewarding place in the Europa League play-off round. That two-legged tie carries a parachute into the Europa Conference League for whoever loses, thus guaranteeing group-stage European football either way. Hearts benefitted from that very filtering process this season when defeat to Swiss champions FC Zurich in August saw them drop into a daunting Conference League group alongside Istanbul Basaksehir, Fiorentina and RFS.

They were runners-up in last season’s Scottish Cup after losing the final to Rangers after extra-time. However, that did not entitle them to a European place. If Scottish Cup winners qualify for the Champions League through Premiership placing, third in the league assumes the cup’s Europa League play-off berth. Last year that was Hearts, who would go on to pocket a £3m-plus profit in the Conference League.

Supporters sang, danced and drank their way around Zurich, Riga, Florence and Istanbul, determined to enjoy the experience of one big Jambo party abroad. Bank balances took a pounding, not to mention livers, amid the joviality. Perhaps some feared it might be a one-off given no Scottish club other than Celtic and Rangers had reached the group stage of any European tournament since Aberdeen in season 2007/08.

Hearts’ hopes of back-to-back group involvement now rest on two issues: Their own ability to retain third spot in the Premiership, plus the drive of Celtic and Rangers to lift the Scottish Cup. Tynecastle officials are acutely aware that they require one of the Glasgow duo to prevail in the final at Hampden on June 3, allied to their side remaining best of the rest in the league.

Celtic and Rangers are destined to take both Scotland’s Champions League spots for season 2023/24 as they sit first and second in the table respectively. So the cup’s European spot would be given to third in table if the silverware stayed in Glasgow. Celtic lead their rivals by nine points, while Hearts are third and a sizeable 25 points behind Rangers with ten games remaining.

Hearts are keen to qualify for European football again.

Odds on the cup heading to either Celtic Park or Ibrox are overwhelming given the remaining teams in the competition are from lower divisions – Inverness Caledonian Thistle, plus whoever progresses from Monday’s quarter-final between Falkirk and Ayr United.

Meantime, all Hearts can do is concentrate on league duties and hope the cup’s latter rounds pan out as expected. If both things fall into place, another Continental adventure will provide cause for celebration in Gorgie.

The permutations needed to guarantee Hearts European group stages with Celtic or Rangers help