It is my birthday and in 15 years’ time, my age will be the square of my age 15 years ago!

Can you work out how old I am?

Now I am thinking “Was there ever a time in my life when I had other special birthdays?”

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…?

Can you make any generalisations about which birthdays are special in this way? Can you prove your findings.

See Solutions and Notes for Teachers

This problem is adapted from the NRICH task How old am I? with permission of the University of Cambridge. All rights reserved.

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