How to change just one side border width of a ttk.Entry?

As stated in my comment before, I'd use a stacked layout with the boxes in frames and the entries in these boxes. So there is no need for special styling. Access to the values within the ttk.Entries gives a dictionary that contains tk.StringVar objects, the keys are uppercase letters 'A'..'I' combined with numbers '1'..'9' like in spreadsheet applications:

import tkinter as tkfrom tkinter import ttkmainWin = tk.Tk()mainWin.title('Sudoku solver')mainFrame = ttk.Frame(mainWin, borderwidth=10)mainFrame.grid(column=1, row=1)# access to entries (of type tk.StringVar)values = {}for box_col in range(3):    for box_row in range(3):        box = ttk.Frame(mainFrame, borderwidth=1, relief='sunken')        box.grid(column=box_col+1, row=box_row+1)        for cell_col in range(3):            for cell_row in range(3):                v = tk.StringVar()                # build spreadsheet key from overall column and row                col = 'ABCDEFGHI'[3*box_col+cell_col]                row = '123456789'[3*box_row+cell_row]                key = col+row                values[key] = v                entry = ttk.Entry(box, width=3, justify='center', textvariable=v)                entry.grid(column=cell_col+1, row=cell_row+1)# example for accessing the entriesvalues['A1'].set(1)values['G3'].set(7)values['E5'].set(int(values['A1'].get())+4)values['I9'].set(int(values['E5'].get())+4)mainWin.mainloop()

Under Windows 8.1, this will look this: