How to create a self resizing grid of buttons in tkinter?

I am trying to create a grid of buttons(in order to achieve the clickable cell effect) with Tkinter.

My main problem is that I cannot make the grid and the buttons autoresize and fit the parent window.

For example, when I have a high number of buttons on the grid, instead of shrinking the buttons so that the grid fits inside the window, I get a stretched frame that goes off screen.

The effect that I am looking for is the grid filling all available space, then resizing its cells to fit within that space. I have read at the documentation, but I still cannot figure out how to make it work.

This is the basic code which is my starting point:

def __init__(self):
    root = Tk()
    frame = Frame(root)
    frame.grid()

    #some widgets get added in the first 6 rows of the frame's grid          

    #initialize grid
    grid = Frame(frame)  
    grid.grid(sticky=N+S+E+W, column=0, row=7, columnspan=2)

    #example values
    for x in range(60):
        for y in range(30):
            btn = Button(grid)
            btn.grid(column=x, row=y)

    root.mainloop()

You need to configure the rows and columns to have a non-zero weight so that they will take up the extra space:

grid.columnconfigure(tuple(range(60)), weight=1)
grid.rowconfigure(tuple(range(30)), weight=1)

You also need to configure your buttons so that they will expand to fill the cell:

btn.grid(column=x, row=y, sticky="news")

This has to be done all the way up, so here is a full example:

from tkinter import *

root = Tk()
frame = Frame(root)
root.rowconfigure(0, weight=1)
root.columnconfigure(0, weight=1)
frame.grid(row=0, column=0, sticky="news")
grid = Frame(frame)
grid.grid(sticky="news", column=0, row=7, columnspan=2)
frame.rowconfigure(7, weight=1)
frame.columnconfigure(0, weight=1)

#example values
for x in range(10):
    for y in range(5):
        btn = Button(frame)
        btn.grid(column=x, row=y, sticky="news")

frame.columnconfigure(tuple(range(10)), weight=1)
frame.rowconfigure(tuple(range(5)), weight=1)

root.mainloop()

@Vaughn Cato gave an excellent answer here. However, he has accidentally included a bunch of extraneous code in his example. Here is a cleaned up and more organized full example doing exactly what his example does.

from tkinter import *

#Create & Configure root 
root = Tk()
Grid.rowconfigure(root, 0, weight=1)
Grid.columnconfigure(root, 0, weight=1)

#Create & Configure frame 
frame=Frame(root)
frame.grid(row=0, column=0, sticky=N+S+E+W)

#Create a 5x10 (rows x columns) grid of buttons inside the frame
for row_index in range(5):
    Grid.rowconfigure(frame, row_index, weight=1)
    for col_index in range(10):
        Grid.columnconfigure(frame, col_index, weight=1)
        btn = Button(frame) #create a button inside frame 
        btn.grid(row=row_index, column=col_index, sticky=N+S+E+W)  

root.mainloop()

Screenshots:

When it first opens (small):

After you maximize the window:

To make the buttons expand when the window is maximized, try to modify the button.grid entry as follows:

btn.grid(column=x, row=y, sticky=N+S+E+W)