Permutations Puzzle (https://puzzling.stackexchange.com/q/114452/5286)

permutations.py

import numpy as np

n = 6
m = 2*(n-1)
maximum = (m*(m+1))//2

target = set(range(1,maximum))

def explore(permutations):
	sums = [ sum(p) for p in permutations ]
	next_num = max(sums) + 1
	
	# If any row is too far behind:
	if any(summe+m<next_num for summe in sums):
		return
	
	# If finished:
	if next_num == maximum:
		sums = {
				x
				for p in permutations
				for x in np.cumsum(p)
			}
		assert(sums) == target
		
		print(permutations)
	
	for i,p in enumerate(permutations):
		# Try generating the next number in the i-th row.
		gap = next_num-sum(p)
		
		if (1<=gap<=m) and (gap not in p):
			permutations[i].append(next_num-sum(p))
			explore(permutations)
			permutations[i].pop()
			# Avoid redundant solutions by exploring first empty row only:
			if not p: break

start = [[1]] + [ [] for _ in range(1,n) ]

explore(start)