Select the figure from among the given option that can replace the question mark (?) in the following series.

Correct — D. Each figure holds eight symbols: one in each of the four corners, and four more across a middle row.

The four figures read:

1 — corners X, = on top and triangle, arrow below, middle row D I N K
2 — corners triangle, X on top and arrow, = below, middle row F N I O
3 — corners F, O on top and N, I below, middle row arrow, triangle, X, =
4 — corners N, F on top and I, O below, middle row S X triangle V

Rule: on this step the corner group and the middle-row group change places, exactly as they did from figure 2 to figure 3. The route, read off that step, is:

middle row left to right goes to the corners anticlockwise from the top left — 1st to top-left, 2nd to bottom-left, 3rd to bottom-right, 4th to top-right
corners read clockwise from the bottom left fill the middle row left to right — bottom-left, top-left, top-right, bottom-right

Apply it to figure 4: S to the top left, X to the bottom left, triangle to the bottom right, V to the top right, and the corners N, F, I, O fill the middle row as I N F O.

That is option (d): S and V on top, X and triangle below, I N F O across the middle.

Why the others are wrong

• (a)
  It leaves X, triangle and V in the middle row, where they already sit in figure 4. At an exchange step every middle-row symbol has to move out to a corner.
• (b)
  Nothing changes group: N, F, I and O are still in the corners and S, X, triangle, V still in the middle. That is the rotation step the series runs on the odd moves, applied one move too late.
• (c)
  Half an exchange: X and triangle do reach the corners correctly, but S and V stay in the middle row and I and O never leave the corners.

The strip alternates two operations. From figure 1 to figure 2, and again from figure 3 to figure 4, the four corner symbols turn one place clockwise. From figure 2 to figure 3 the corner group and the middle-row group trade places.

Figure 4 to the answer is therefore a trade, and the exact routing can be copied from the trade already on the page rather than guessed.

Two symbols also retire and two new ones enter at each turning step — D and K leave and F and O arrive between figures 1 and 2, and the arrow and = give way to S and V between figures 3 and 4. The trade step moves symbols instead of replacing them, so the answer uses figure 4's eight symbols and no others.

Key facts

• Figure 4 has N and F across the top, I and O across the bottom, and S X triangle V through the middle.
• In the figure 2 to figure 3 exchange, the middle row F N I O landed at top-left, bottom-left, bottom-right and top-right in that order.
• The corners of figure 2, read clockwise from the bottom left as arrow, triangle, X, =, became the middle row of figure 3 in that order.

Common traps

• Assuming every step of a figure series repeats the same operation
• Rotating the corners because that is what worked from figure 3 to figure 4
• Checking the corners and ignoring the order of the middle row

No directly related past PYQ was found.