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.
“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.” culegere matematica clasa a 9 a
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. One rainy Thursday, he flipped to a random page
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. Find their ages
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.
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: