Mad Bomber - Proof | Python Fiddle

import math as m
import random as r

bombs = 5
board = [30,30,5]
iboard = [0,0,5]
targets = len(board)

dist = [[bombs]]
lst = [bombs]

while len(lst) < bombs:
	idx = list(lst+[1]).index(1) - 1	# index of last non-1 value
	oval = lst[idx]											 # last non-1 value
	tval = oval - 1											 # target max value of collapse
	total = sum(lst[idx:])								# sum of collapse (of lst, from idx to end, inclusive)
	# print("LIST: " + str(lst))
	# print(" oVal: " + str(oval))
	# print(" tVal: " + str(tval))
	# print(" Totl: " + str (total))
	lst = lst[:idx]											 # remains of collapse (lst, up to idx, non-inclusive)
	cotton = list(int(tval) for i in range(0,int(total/tval)))
	tail = total % tval
	if tail:
		lst += cotton + [tail]
	else:
			lst += cotton
	dist += [lst]
				
# print()
for i in dist:
	i.sort()
#	print(i)
# print("TOTAL DISTRIBUTIONS: " + str(len(dist)))

invalid = []
for i in dist:
	if len(i) > targets:
		invalid += [i]
		# (str(i) + "c INVALID: " + str(i))
	else:
		for j in range(len(i),targets):
			i += [0]
		i.sort()
		# print(str(i)  + "c VALID: " + str(i))

for i in invalid:
	dist.remove(i)
# print()
# for i in dist:
# 	print(i)
# print("VALID DISTRIBUTIONS: " + str(len(dist)))
perms = []

for i in dist:
	pt = list(i)
	# print("++ " + str(perms) + " + " + str(pt))
	# print(" = " + str(perms))
	while next:
		# input(dist)
		# print(str(perms) + " + " + str(pt))
		perms.append(list(pt))
		idx = len(pt) - 1
		while pt[idx] >= (pt + [pt[-1]])[idx+1]:
			# print(idx)
			idx -= 1
			if idx < - len(pt):
				break
			# print(idx)
		if idx < 0:
			break
		idx0 = idx
		idx1 = len(pt) - 1
		while pt[idx0] >= pt[idx1]:
			idx1 -= 1
		tmp = pt[idx0]
		pt[idx0] = pt[idx1]
		pt[idx1] = tmp
		# print(str(idx0) + " <-> " + str(idx1))
		# print(str(pt[idx0]) + " <-> " + str(pt[idx1]))
		rem = pt[:idx0+1]
		rev = pt[idx0+1:]
		rev.reverse()
		# print(str(rem) + " + " + str(rev))
		pt = rem + rev
		# print("  p" + str(perms) + " + " + str(pt))
		# print(" + " + str(pt))

# print()
# for i in perms:
#	print(i)
# print("POSSIBLE OUTCOMES FOR " + str(bombs) + " BOMBS OVER " + str(targets) + " TARGETS: " + str(len(perms)))

invalid = []
for i in perms:
    if sum(i[j] > board[j] for j in range(0,targets)):
        invalid += [i]
    
iper = 0    
for i in perms:
    chk = 1
    for j in range(0,targets):
        chk *= i[j] >= iboard[j]
    iper += chk

ostr = "CUR: "
for i in board:
    ostr += "0"[:i < 10] + str(i) + " "
tstr = "TGT: "
for i in iboard:
    tstr += "0"[:i < 10] + str(i) + " "
print("BMBS: " + str(bombs))
print(ostr)
print(tstr)
perc = 100*float(iper)/len(perms)
print("PROBABILITY: " + str(round(perc,3)) + "% ( " + str(iper) + " / " + str(len(perms)) + " )")

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