Culegere Matematica Clasa A 9 A [cracked] May 2026

He checked twice. No mistake. He checked the answer key at the back—it only said “Impossible. Explain why.”

He wrote the equations: let son = s , father = f . (f = 4s) (f + 18 = 2(s + 18) \Rightarrow 4s + 18 = 2s + 36 \Rightarrow 2s = 18 \Rightarrow s = 9, f = 36.) Sum = (9 + 36 = 45), which is not prime. A contradiction. culegere matematica clasa a 9 a

He had learned something the culegere never said out loud: sometimes the right answer is that there is no answer—and explaining why is the real solution. He checked twice

That night, he didn’t stop at three problems. He solved five. Then ten. By December, the blue culegere was battered but beloved. And when his teacher asked the class, “Who enjoys the challenge problems at the end of each chapter?” Andrei raised his hand. Explain why

“The equations force the son to be 9 and the father 36, with sum 45. Since 45 is composite (3 × 15, 5 × 9), the condition ‘sum is prime’ cannot be met. Therefore, no such ages exist in whole numbers.”

“Easy,” Andrei muttered. Let the son be x , the father 3x . In 12 years: (3x + 12 = 2(x + 12)). He solved it: (3x + 12 = 2x + 24 \Rightarrow x = 12). Father 36, son 12. Done.