Sampling Sunflowers

A British farmer grows sunflowers for making sunflower oil. Her field is arranged in a grid pattern, with 10 rows and 10 columns as shown in the figures below. Irrigation ditches run along the top and bottom of the field. The farmer would like to estimate the number of healthy plants in the field so she can project how much money she'll make from selling them. It would take too much time to count the plants in all 100 squares, so she'll accept an estimate based on a sample of 10 squares. Which sampling method will give her the best estimate?

For a more detailed discussion, see the description in The Practice of Statistics, Statistics and Probability with Applications, or Introductory Statistics: A Student-Centered Approach.