Matchsticks in a pattern — Aptitude Question
Matchsticks in a pattern: Squares are built in a row from matchsticks: 1 square needs 4 sticks, 2 squares need 7,… Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Squares are built in a row from matchsticks: 1 square needs 4 sticks, 2 squares need 7, and 3 squares need 10. How many sticks are needed for 10 squares?
Options
- 28
- 31
- 34
- 40
Show the answer and the worked solution
Correct answer: B. 31
Worked solution
- The counts go 4, 7, 10 — rising by 3 each time.
- The formula is 3n + 1.
- For 10 squares: 3 × 10 + 1 = 31.
Answer: 31.
The idea
Find the constant increment first, then fit the linear rule an + b using one known value. Multiplying 4 by 10 ignores the shared sides.
Shortcut. Ten separate squares would need 40 sticks, but the 9 walls between neighbours are shared, so 40 − 9 = 31.
Common trap. "40" — multiplying 4 sticks by 10 squares, which counts each of the 9 shared walls twice.