Question

In the sequence of tiles shown below, the missing tile indicated by the question mark should be

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Split the tiles into odd positions (1st, 3rd, 5th) and even positions (2nd, 4th), and look for a squared-number rule running on each group separately.

Answer 1

The Correct Option is B

Step 1: Count the dots in each visible tile.
Reading the five tiles from left to right, the 1st tile has 2 dots, the 2nd tile has 3 dots, the 3rd tile is the missing one, the 4th tile has 6 dots, and the 5th tile has 10 dots.

Step 2: Split the tiles into two interleaved groups.
Look at the odd-position tiles (1st, 3rd, 5th) as one group and the even-position tiles (2nd, 4th) as a second group, since many figure-series questions run two simple rules in parallel on alternate positions.

Step 3: Find the rule for the odd-position group.
The 1st tile has 2 dots and the 5th tile has 10 dots. Test the rule "dots = (rank)^2 + 1", where rank counts 1, 2, 3 for the 1st, 3rd, and 5th tiles in this group.
\[ 1^2+1=2 \, (\text{1st tile, matches}) \]
\[ 3^2+1=10 \, (\text{5th tile, matches}) \]
Since the rule holds at both known points, the 3rd tile (the missing one, rank 2 in this group) must have \(2^2+1=5\) dots.

Step 4: Check the rule against the even-position group.
The 2nd tile has 3 dots and the 4th tile has 6 dots. Test the rule "dots = (rank)^2 + 2", with rank 1, 2 for the 2nd and 4th tiles.
\[ 1^2+2=3 \, (\text{2nd tile, matches}) \]
\[ 2^2+2=6 \, (\text{4th tile, matches}) \]
This confirms two clean parallel rules are running on alternate tiles, which supports the answer found in Step 3.

Step 5: Match to the options.
The missing tile needs exactly 5 dots. Option (A) shows 4 dots, option (B) shows 5 dots arranged as two dots on top, one in the middle, and two on the bottom, option (C) shows 6 dots, and option (D) shows more than 5 dots. Only option (B) has 5 dots.

Final Answer:
The missing tile has 5 dots. \[ \boxed{\text{Option (B)}} \]