Springboks' World Cup permutations: Boks almost certain of quarter-final spot

The Boks knew they needed a bonus-point win against Tonga in Marseille on Sunday, preferably with as large a margin of victory as possible, to give themselves every chance of advancing to the knockout stages in France.

While Tonga produced their best performance of the tournament thus far and did not make life easy for Jacques Nienaber's men, South Africa were still able to get the job done by bagging all five points in a 49-18 victory.

Crucially as well, the 31-point margin of victory means they are almost certain to make it through, with only a very unlikely mathematical outcome in next weekend's clash between Ireland and Scotland set to deny them.

The Permutations

The Boks are currently leading Pool B with 15 points, having played all four of their matches. Ireland are one point back on 14, with a game to come against Scotland, who are on 10 points. The Boks have a positive points difference of 117, while Ireland are on 122 and Scotland on 97.

To put it simply, Scotland would need to secure a bonus-point against Ireland for scoring four tries while also beating Andy Farrell's men by a margin of 21 points to move ahead of the Springboks.

That's incredibly unlikely in itself, but what's even more unlikely is that Ireland would still need to bag a bonus point of their own for scoring four tries, despite getting tonked by 21 points, or they would be the ones going out - not the Boks.

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It doesn't take a mathematical genius to deduce the likelihood of such an outcome: virtually slim to none, meaning the Springboks can rest easy for the next seven days, safe in the knowledge they've done what they needed to do.

Scotland will know their only realistic chance of advancing is by beating Ireland with a bonus point and somehow denying their opponents one. Which would see the Boks top the pool, with Scotland advancing in second.

Of course, given the form of Andy Farrell's side, the most likely outcome next weekend in Paris is an Irish victory, which means the Boks would still advance by finishing second in the group, regardless of any bonus-point or points difference permutations.

One thing is clear, however - it's Scotland and Ireland who have the far more nervous week ahead, to say nothing of the massive challenge that awaits them both at the Stade de France on Saturday.

The Springboks, on the other hand, have two weeks in which to rest, recuperate and work on their plans for the quarter-final matchup that almost certainly awaits.

READ MORE: Jacques Nienaber salutes Springboks for getting the job done against Tonga