The Doomsday rule is a mental algorithm used to calculate the day of the week for any given date. It was developed by mathematician John Horton Conway and is based on the idea that certain anchor days, or "doomsdays," recur each year. By memorizing these anchor days and applying simple calculations, one can quickly determine the day of the week for any date. To use the Doomsday rule, you first identify the anchor day for the century and then find the doomsday for the specific year. By comparing the date to known doomsdays, you can easily find the corresponding day of the week. This method is particularly useful for quick mental calculations.