Victor Gutenmacher sent me this great puzzle. It appeared on a
job interview in an insurance company.

In each equation below, insert one or more mathematical symbols to make the equation correct. You may use the symbols +, -, *, / sqrt, (, ), and the decimal point (e.g. you may insert a decimal point before 1 to get .1.)

1 1 1 = 3

2 2 2 = 3

3 3 3 = 3

4 4 4 = 3

5 5 5 = 3

6 6 6 = 3

7 7 7 = 3

8 8 8 = 3

9 9 9 = 3

For example, 1 + 1 + 1 = 3 and sqrt9 – sqrt9 + sqrt9 = 3.

Victor's friend, Benjy, came up with a solution which, amazingly,
is given by one formula, f(n) where n = 1, 2, … , 9. See if you can find it.