At times during the build-up to Scotland’s nerve-shredding Pool B decider against Ireland, it has felt like a maths degree would be useful to work out the various permutations.

For the Irish though, things are simpler – just win. If they do that, they will go through as Pool B winners, with a likely quarter-final against New Zealand awaiting them.

Winning isn’t exactly a novelty to Andy Farrell’s team either. They head into Saturday’s crunch clash at the Stade de France on the back of a record 16-game winning streak that has propelled them to the No. 1 spot in the world rankings.  

Beating Scotland has become a habit too, with the men in green coming out on top in their last eight meetings with their Celtic cousins.

For head coach Andy Farrell, then, the message is a simple one – even if they have a helping hand ready to talk through the more complicated permutations if the need arises.

“We want to win. It’s a massive game, so important to us and obviously to the travelling fans and the people back home,” Farrell said.  

“Fortunately, we have Iain Henderson who is good at maths, so we are across everything as far as that's concerned.

“But the easiest thing is to make sure we perform well and deserve to win the game outright."

Farrell made two changes to his side for the battle with the Scots, calling numbers man Henderson into the second row and starting Dan Sheehan at hooker.

But the game will be a landmark moment for a mainstay of this all-conquering Irish side, flanker Peter O’Mahony, who will win his 100th Ireland cap when he runs out in Paris.

"We could sit here all day and talk about what he brings and means to us all, what type of bloke he is, the family man he is,” Farrell said.

“He’s selfless. You guys see his performances on the pitch and what it means for him to play for Ireland but behind the scenes, he is definitely, 100 per cent, the best I have ever seen at making the dressing room feel right.

"It is him being himself because he’s genuine. There’s no better man you’d want sat alongside you than Peter O’Mahony. He’s a selfless player who gives everything to his team-mates and backs that up with consistent performances week in, week out."

One blow Farrell had to contend with was the loss of centre Robbie Henshaw to a hamstring issue, who has been replaced on the bench by Stuart McCloskey.

“They want to see how things settle down and it probably takes about five days for that to happen with an issue like his, but it looks like it could be a minimum of a couple of weeks at this stage,” Farrell added.

As for James Ryan, there was no physical concern behind the decision to drop him to the bench for Henderson.

"James is fit. He had a bit of niggle on his wrist but he has trained the house down, the best I have seen him train in a good amount of years yesterday,” Farrell said.

“He nearly took Johnny's [Sexton] head off three or four times so he is fit and raring to go."

Sexton, head safely still on shoulders, will orchestrate Ireland’s bid to reach the knockout stages from fly-half, where a fascinating battle of styles and skills promises to break out against Finn Russell.

But the 38-year-old Irish captain, who will retire after the World Cup, doesn’t buy into the idea of an individual contest between the two playmakers.

"Like I have said any other time I’m asked about the opposition fly-half, it’s never us against each other, it’s our teams and you rely so much on guys around you,” said Sexton.

“You tackle each other very rarely anyway. We are both in charge of our teams and he is an outstanding player. He has got a full bag of tricks, and we have to prepare for that."

Ireland underlined their credentials as potential World Cup winners by beating reigning champions South Africa 13-8 in a brutal but brilliant match at the Stade de France two weeks ago.

It was an intensely physical contest, packed with dominant tackles and ferocious breakdown battles, but Ireland have since had a rest week to recover and Sexton reassured Irish fans about his condition.

Asked how he is physically, Sexton said: "Good. The South Africa game was definitely the most physical since my return.

“It was tough but the week off came at a good time. We had a few days to chill out and unwind before we started building up again for this massive game."

Ireland sit top of Pool B going into the decider against Scotland with a perfect record of three wins from three, their success against the Springboks coming after comfortable victories against Romania and Tonga.