Which figure should replace the question mark (?) if the following series were to be continued?

Correct — D. Rule: the moves alternate — figure 1 to 2 makes the same change as figure 3 to 4, so figure 4 to the answer repeats the change from figure 2 to 3.

That change is two rotations running at once.

Top loop: top-centre goes to mid-left, mid-left to top-right, top-right to top-centre.
Lower-right 2×2 block (mid-centre, mid-right, bottom-centre, bottom-right) turns one place clockwise.

Figure 4 reads B ▽ on top, Z ↑ X across the middle, D C below. The top loop sends ▽ to top-centre, Z to top-right and B to mid-left. The block sends D to mid-centre, ↑ to mid-right, X to bottom-right and C to bottom-centre.

That gives ▽ Z on top, B D ↑ across the middle and C X below — option (d).

Why the others are wrong

• (a)
  It puts ▽ and ↑ in the right cells and then scrambles the letters. Its 2×2 block holds Z and B, which were nowhere near that block in figure 4, and a turn cannot import a symbol from outside itself.
• (b)
  Its ▽ sits at bottom-right. In all four given figures ▽ stands in the top row, and neither of the two rotations moves anything from the top row down to the bottom one.
• (c)
  It gets the top three cells right — ▽, Z, B — but turns the 2×2 block anticlockwise: mid-centre to bottom-centre, bottom-centre to bottom-right. Figure 2 to 3 turns that block the other way.

A figure series whose cells never change shape is a permutation puzzle. The same seven symbols occupy the same seven cells in every box, and only the arrangement moves.

Do not force one rule onto every step. When 1 to 2 and 3 to 4 agree with each other but not with 2 to 3, the series is alternating, and the missing box repeats the even step.

Work symbol by symbol rather than picture by picture. Note where each of ▽, ↑, B, C, D, X and Z stands in figures 2 and 3, and the two loops fall out — a three-cell loop across the top and a four-cell turn in the lower-right block.

Key facts

• The same seven cells are filled in every figure, so only the arrangement changes.
• Figure 1 to 2 and figure 3 to 4 apply the same movement.
• Figure 2 to 3 rotates top-centre, mid-left and top-right, and turns the lower-right 2×2 block clockwise.
• ▽ stands in the top row in all four given figures.

Common traps

• Forcing one rule onto every step and then picking whichever option is nearest
• Turning the 2×2 block the wrong way round, which lands you on option (c)
• Reading the grids row by row instead of tracking where each symbol goes

No directly related past PYQ was found.