A solution for https://stackoverflow.com/questions/54271178/build-a-plinko-board-of-words-from-a-dictionary

word2.py

import sys

L0 = sys.argv[1]
N = int(sys.argv[2])

alpha = set("abcdefghijklmnopqrstuvwxyz")

words = set()
for L in open("words_alpha.txt"):
    L = L.strip()
    if len(L) == N and L[0] == L0:
        words.add(L)

print("%i acceptable words" % len(words))

wsets = {}
for i in range(1, N):
    for c in alpha:
        wsets[(i, c)] = set(w for w in words if w[i] == c)

#
#  playing board
#
#  x
#  x x
#  x x x
#  x x x x
#  x x x x x
#

M = [["?"] * (i+1) for i in range(N)]

wtab = []
for i in range(1<<(N-1)):
    j = 0
    w = [(0, 0)]
    for k in range(N-1):
        j += (i>>k)&1
        w.append((k+1, j))
    wtab.append(w)

def show():
    for i, L in enumerate(M):
        print(" " * (N-i) + (" ".join(L)))

def solve():
    if M[0][0] == "?":
        # First word, write it down on left side
        for w in words:
            for i in range(N):
                M[i][0] = w[i]
            if solve():
                return True
        for i in range(N):
            M[i][0] = "?"
        return False
    elif M[1][1] == "?":
        # Second word; consider words where the
        # second character is bigger than the second
        # character of first word and write them down
        # on the right side.
        for w in words:
            if (w[1] > M[1][0]):
                for i in range(1, N):
                    M[i][i] = w[i]
                if solve():
                    return True
        for i in range(1, N):
            M[i][i] = "?"
        return False
    else:
        # General case; find a free cell and try every compatible
        # letter that covers it.
        free = None
        for i in range(2, N):
            for j in range(i):
                if M[i][j] == "?":
                    free = (i, j)
                    break
            if free: break
        if free is None:
            # No free cells, we solved the puzzle
            return True
        i, j = free
        checks = [w for w in wtab if (i, j) in w]
        for x in alpha - set(M[i]):
            M[i][j] = x
            for w in checks:
                if (i, j) in w:
                    word = "".join(M[ii][jj] for (ii, jj) in w)
                    if "?" not in word:
                        if word not in words:
                            break
                    else:
                        ws = None
                        for ii in range(1, N):
                            if word[ii] != "?":
                                if ws is None:
                                    ws = wsets[ii, word[ii]]
                                else:
                                    ws = ws & wsets[ii, word[ii]]
                                if not ws: break
                        if not ws: break
            else:
                # Acceptable assignment, recurse
                if solve():
                    return True
        M[i][j] = "?"
        return False

def score(debug = False):
    miss = 0
    for w in wtab:
        word = "".join(M[i][j] for (i, j) in w)
        if word not in words:
            miss += 1
        if debug:
            print("Checking " + word)
    return miss

if solve():
    show()
    score(True)
else:
    print("No solution")