I remarked to a friend how surprised I was to learn that as few as 23 randomly chosen people give better than even odds of a shared birthday. She agreed, saying three of her friends shared her birthday. The product of their ages is 2450 cubic years, she said, and their sum, remarkably, is twice your age [meaning mine.] It was a statement, to be sure, but I knew from the twinkle in her eye it was also a challenge.

I scribbled on the back of an envelope for a moment. Well? she smiled, got you stumped? In fact I could not answer. I'm afraid I need another clue. OK, she said, I am older than any of the three, and my age is equal to the product of the ages of the two youngest.

Triumphantly I announced the ages of her three friends.

I remarked to a friend how surprised I was to learn that as few as 23 randomly chosen people give better than even odds of a shared birthday. She agreed, saying

threeof her friends sharedherbirthday. The product of their ages is 2450 cubic years, she said, and their sum, remarkably, is twiceyourage [meaning mine.] It was a statement, to be sure, but I knew from the twinkle in her eye it was also a challenge.I scribbled on the back of an envelope for a moment. Well? she smiled, got you stumped? In fact I could not answer. I'm afraid I need another clue. OK, she said, I am older than any of the three, and my age is equal to the product of the ages of the two youngest.

Triumphantly I announced the ages of her three friends.

p.s. That's a challenge.

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