“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.
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: culegere matematica clasa a 9 a
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. “Easy,” Andrei muttered
Andrei hated the culegere . Its thick, blue cover—creased at the spine, coffee-stained on the back—sat on his desk like a small, mute tyrant. His father had bought it in September with the best intentions: “Three problems every night, and you’ll be top of the class.” He solved it: (3x + 12 = 2x + 24 \Rightarrow x = 12)
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.
He checked twice. No mistake. He checked the answer key at the back—it only said “Impossible. Explain why.”
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.