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He felt a strange thrill. The problem hadn’t tricked him—it had invited him to think beyond the formula. For the first time, math felt less like memorizing and more like investigating.
But the next problem stopped him cold. Problem 790: A different father is four times as old as his son. In 18 years, he will be only twice as old. But the sum of their current ages is a prime number. Find their ages.
“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. culegere matematica clasa a 9 a
He checked twice. No mistake. He checked the answer key at the back—it only said “Impossible. Explain why.”
Andrei stared at the page. For the first time, the culegere wasn’t asking for a number. It was asking for a reason . He wrote in his notebook: He felt a strange thrill
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.
But by October, the culegere had become a symbol of failure. Problem 347: Solve the system of equations . He’d stare at the two innocent-looking lines until the x’s and y’s blurred. Problem 512: Study the monotonicity of the function . The arrows (↑ for increasing, ↓ for decreasing) felt like personal accusations. But the next problem stopped him cold
One rainy Thursday, he flipped to a random page. Problem 789: A father is three times as old as his son. In 12 years, he will be twice as old. Find their ages.