A Special Squarish Age


I got this problem from Rustan Leino, who says Chuck Chan created it and Greg Nelson suggested introducing the name "squarish" to simplify the problem statement.

I solved it and wrote up my solution.


Let's say that a number is squarish if it is the product of two consecutive numbers. For example, 6 is squarish, because it is $2 \times 3.$

A friend of mine at Microsoft recently had a birthday. They said their age is now squarish. Moreover, since the previous time their age was a squarish number, a squarish number of years have passed. How many years will they have to wait until their age will have this property again?

Solution     Reveal