Math puzzle: A sequence of odd events
From left: Snezhana Kudryavtseva/iStock/Getty Images Plus; Cavan Images/Cavan/Getty Images Plus; Tatiana Sviridova/Moment/Getty Images Plus
In Spring 2025, we — Lilly Fang, Lester Mackey and our two children — noticed that something odd was happening to our family. First, Noah turned the odd age of 9 in May. Then Isaiah turned odd — or, more specifically, 7 — in August. Next, Lilly turned odd, 41, in November and finally, Lester turned odd, also 41, in February. This led us to wonder…
- Does every family experience an “odd cycle,” in which the age of each member flips from even to odd in turn?
- With a list of birthdays and birth years for all members of a given family, what is a simple way to determine whether (a) the family will experience an odd cycle and (b) in what order the members will flip from an even age to an odd one?
- Why was Noah the first to turn an odd age and not Lilly (who was born first) or Lester (who has the earliest birthday each year)?
- Is there a simple way to check 2(a) and 2(b) without calculating anyone’s age?
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