1) If you fix a string on two sides, draw what the longest "standing wave" could look like. What is the wavelength for this wave, compared to the length of the string?
2) Now consider a string with one free end. A free end is always at a peak or valley, since that is the only way forces can balance at the end of the string without something holding the other side. Draw the longest resonant wavelength that will fit properly on this string.