Group the given figures into three classes using each figure only once.

Concept: In a figure-classification set, ignore the small shape drawn inside each figure and look only at the outermost boundary shape together with the internal line pattern that always accompanies it — a rectangle is always crossed by its two diagonals, a triangle is always crossed by its three medians (each vertex joined to the midpoint of the opposite side), and a circle is always crossed by two mutually perpendicular diameters. Two figures belong to the same class only when they share this outer shape plus line pattern; the smaller shape nested inside each figure is a decoy and is allowed to differ.

Application: Sorting all nine figures by their outer boundary shape gives:

So the three classes are the triangles (2, 6, 9), the rectangles (1, 5, 7), and the circles (3, 4, 8) — exactly the grouping 2,6,9 ; 1,5,7 ; 3,4,8.

Note: sorting by the shape nested inside each figure instead (2,4,7 / 1,8,9 / 3,5,6) also happens to split the nine figures into three groups of three — but the outer boundary shape, not the inner decoration, is the feature that stays fixed across every valid class in this puzzle type; the inner shape is deliberately varied precisely so it cannot be used as the classification key.

Cross-check against the other groupings:

• 2,4,7 ; 1,8,9 ; 3,5,6 — all three classes here mix figures from three different outer shapes at once (a triangle, a rectangle, and a circle in the very same class), so none of the three groups is built on a shared outer shape.

• 2,6,7 ; 1,5,8 ; 3,4,9 — each class here almost works, with two of its three figures sharing an outer shape, but every class still carries one figure whose outer shape does not match the other two.

• 2,8,7 ; 1,5,9 ; 3,4,6 — one class here mixes three different outer shapes together, and the other two classes each carry one figure whose outer shape does not match its two classmates.