NRICH: How Old Am I?

In 15 years’ time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

On my last birthday, my friend said to me:

“In 15 years’ time, your age will be the square of your age 15 years ago!”

Can you work out how old I am?
This got me thinking…

Was there ever a time in my life when I had other birthdays that were special in this way?

Could I have said:
“In 3 years’ time, my age will be the square of my age 3 years ago”
or:
“In 4 years’ time, my age will be the square of my age 4 years ago”
or:
“In 5 years’ time, my age will be the square of my age 5 years ago”
or:
“In 6 years’ time, my age will be the square of my age 6 years ago”
or…?

Can you make any generalisations about which birthdays are special in this way?

Can you prove your findings?

Age 14 to 16


Algebra & Pre-Algebra, Equations
High School, Educator

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NRICH (University of Cambridge)

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Challenge
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Click here for a poster of this problem.