Which option replaces the question mark shown above? Find the tile pair that…
2023
Which option replaces the question mark shown above? Find the tile pair that correctly completes the series.
Attempted by 200 students.
Show answer & explanation
In a dot/domino sequence-series question, the tiles are split into groups by the vertical dividers, and each group follows its own fixed step rule (dot counts rising or falling by a constant amount tile to tile). When groups alternate between a falling and a rising rule, first read off the exact step rule from the group(s) whose tiles are all visible, then apply that same alternation to extend the incomplete group -- even when the missing part of a group is shown as a single placeholder standing in for more than one tile.
Group 1 (three full tiles): (3,2) -> (2,1) -> (1,0). Both the top and bottom dot counts fall by exactly 1 at every step, so Group 1's rule is "decrease by 1 each tile".
Group 2 (three full tiles): (0,1) -> (1,2) -> (2,3). Both counts rise by exactly 1 at every step, so Group 2's rule is "increase by 1 each tile", the opposite of Group 1.
The groups alternate: fall, then rise. So Group 3 must switch back to the falling rule used in Group 1.
Group 3 is shown with only its last tile, (1,0), given; the question mark stands for the two tiles before it, so Group 3 (like Groups 1 and 2) is a three-tile group with its first two tiles missing.
Applying the same "decrease by 1 each tile" rule and working backward from the given last tile (1,0): the tile just before it must be (2,1), and the tile before that must be (3,2).
So the two tiles that replace the question mark, read left to right, are (3,2) then (2,1), which continues into the given (1,0) -- reproducing Group 1's progression exactly.
Cross-check with the total dot count per tile: Group 1 totals 5, 3, 1; Group 2 totals 1, 3, 5 (the mirror image); a Group 3 built from (3,2), (2,1), (1,0) totals 5, 3, 1 again, exactly mirroring Group 1 -- confirming the pair (3,2) then (2,1) is consistent with the rest of the series.
Therefore, the pair of tiles that completes the series is (3,2) followed by (2,1) -- the tile showing three dots over two dots, then the tile showing two dots over one dot.