Problem 9 · Test a pattern against examples and counterexamples · 3 points
Made by AI and not reviewed by a real person.
Mia’s number box accepts 9, 25, 49, and 81, but rejects 16, 35, 64, and 99. Which number below would it accept?
- 121
- 144
- 120
- 100
- 143
Show a hint
- Try arranging the numbers in equal rows and columns. Some rejected numbers can be arranged that way too, so look more closely.
- Compare the side lengths of square arrays for accepted numbers with those for 16 and 64.
Show the answer and solution
Answer: A — 121
The accepted numbers are squares with odd side lengths: 3 × 3, 5 × 5, 7 × 7, and 9 × 9. So 121 belongs because it is 11 × 11. The tempting choice 144 is also a square, but its side length is even: 12 × 12. The same is true of 100 = 10 × 10. Neither 120 nor 143 is a square: 120 lies between 100 and 121, while 143 lies between 121 and 144.