Data Validation Depending On Column

Let's say I have data validation on column A, which only allows 2 values, "Number" and "Letter". Easy enough. If the value "Number" is selected in A1, when the user moves to B1, I want a validation list of 1,2 and 3, when they move to C1, I want a list of 4, 5 and 6 and when they move to D1, a list of 7, 8 and 9. However, if "Letter" is selected in A1, when the user moves to B1, I want a list of R, S and T, when they move to C1, U, V and W, and when they move to D1, a list of X, Y and Z. I tried using dependant validation, but can only get all three columns (B, C and D) to either be 1, 2 and 3, or R, S and T. The validation lists would be existing named ranges on a separate sheet.