Find-My-Age Puzzle (True Facts): The Olson Brothers
Three brothers born on January 1st; one year one brother's age is half the sum of the other two. When does it happen again? Solution on the full series page.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2024-01-01-find-my-age-puzzles-but-with-all-true-facts--find-my-age-puzzle-true-facts-the-olson-brothers/ (CC BY-NC 4.0)Transcript
The Olson Bros: three brothers all born on January 1st in different years. One year, one brother's age was precisely half the sum of the other two. How many years would pass before this happened again?
[Solutions] Ja Rule was born on Leap Day, 1976; his "sixth birthday" was the day he turned 24. · Hopkins (born Dec. 31): on Dec. 30 he was 48; on Dec. 31 he turned 49; on Jan. 1 the fare went up; that year he turned 50; the next year, 51. · From 63 BCE to 14 CE is 76 years; there was no year zero. · The only square between 1800 and 1900 is 43² = 1849, so De Morgan was born in 1806. · If this is true one year, it's true every year.