In the sequence of tiles shown below, the missing tile indicated by the question mark should be:
Show Hint
Hint:
Count the dots in the tiles you can already see (2, 3, then a gap, then 7, 11) and check whether these numbers share a special property, such as all being prime, rather than following a simple addition pattern.
Step 1: Count the dots in each tile.
Reading the row left to right: tile 1 has 2 dots, tile 2 has 3 dots, tile 3 is missing, tile 4 has 7 dots (three across the top, one in the middle, three across the bottom), and tile 5 has 11 dots (four across the top, three in the middle row, four across the bottom). So the known totals in order are 2, 3, ?, 7, 11.
Step 2: Recognize the sequence.
2, 3, 7, and 11 are each prime numbers, numbers with no divisors other than 1 and themselves. Reading them as consecutive primes: 2 is the 1st prime, 3 is the 2nd prime, 5 is the 3rd prime, 7 is the 4th prime, 11 is the 5th prime. Tile 3 sits in the 3rd position, so it should carry the 3rd prime number, which is 5.
Step 3: Match this to the dot counts shown in the options.
Option (A) shows 4 dots, option (B) shows 5 dots arranged as 2 dots on top, 1 dot in the middle, and 2 dots on the bottom, option (C) shows 6 dots, and option (D) shows 8 dots. Only option (B) carries 5 dots, matching the missing prime.
Step 4: Rule out the remaining options.
4 is not prime, since it splits evenly as 2 times 2. 6 is not prime, since it splits evenly as 2 times 3. 8 is not prime, since it splits evenly as 2 times 4. None of these fit the prime-number rule that ties tiles 1, 2, 4, and 5 together, so only the 5-dot tile completes the sequence.
Final Answer:
The dot counts across the row are the first five prime numbers, 2, 3, 5, 7, 11, so the missing tile has 5 dots, matching option (B).
\[ \boxed{\text{Option (B)}} \]
