1331.11 – Guess My Age!

Tags:Problem Set 13Algebra IAlgebra

Everybody loves Stella's Dutch neighbor Saartje. (That's Sar'-tia). Saartje's age is a perfect square greater than another perfect square and also a perfect square less than a perfect square. Furthermore, next year her age will be a prime number. So how old is she?


One way to go is just to try possibilities. The primes less than 50 are 47, 43, 41, 37, and so forth down to 11, 7, 5, 3, 2. The number 40 works: it is 9 less than 49 and 4 more than 36. Are there any others?