One of the more intriguing arithmetic puzzles at this summer's World Cup concerns the third-place standings across all groups — and whether a team could advance to the round of 32 without even reaching three points.

The answer, perhaps surprisingly, is yes. Because the six worst third-placed finishers are eliminated while the best four advance, the mathematics of specific group outcomes can allow a team with only one or two points to sneak through.

How the third-place rankings work

All third-placed sides are ranked against one another regardless of the strength of their respective groups. That creates a situation where a team with three points could be knocked out — while a rival with fewer points, finishing third in a more competitive group, advances.

The scenario came into focus during Group C, where Haiti briefly threatened to finish with three points and still exit the tournament. Morocco's two second-half comebacks ultimately secured the win, but the broader arithmetic question remains alive across several groups.

Which groups could produce a low-points third-place qualifier?

Several groups still hold the mathematical possibility of a third-place finish with fewer than three points:

Group A: A third-place finish on just 1 point is possible if Mexico beat Czech Republic and South Korea beat South Africa. A draw in either match pushes that minimum up to 2 points.

Group E: The same logic applies, with Curacao facing Ivory Coast and Ecuador facing Germany as the pivotal fixtures.

Group G: A 2-point third-place finish remains possible if New Zealand beat Belgium, or if Egypt beat Iran, or both.

Group H: A side could finish third on 2 points if Uruguay lose to Spain.

Group I: A 1-point third-place finish is possible if Senegal and Iraq draw with one another.

Group K: A 2-point finish is on the cards if DR Congo and Uzbekistan draw.

The bottom line

If five of those six scenarios come to pass, one team with 2 points will advance to the round of 32. If all six materialise, two teams on 2 points will reach the knockouts. However, the numbers rule out any possibility of a team progressing as a third-placed side on just 1 point — that outcome cannot survive the full ranking comparison.

Already-eliminated Turkiye offer a neat illustration of the cruelty involved: a win over the United States on Thursday would leave them with 3 points and still out of the tournament.