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How many paths the snake in the Snake game can take?

How many paths the snake in the Snake game can take? I was given this challenge last week and I thought I would share my way of solving it with you all Y'all know the famous game "Snake", so no need for an introduction now. The question is easy: given the position of the snake within a map of known size and the number of movements the snake can do, how many distinct paths can the snake follow without intersecting itself and without going out of the map's boundaries? Maybe once you go over it the question is not as easy as it sounds, so let's illustrate it with an example. Let's imagine we have a map that contains 4 rows and 3 columns, like the one below. And let's imagine that we have a snake whose body occupies the following cells: [(2,2),(3,2),(3,1),(3,0),(2,0),(1,0),(0,0)]. The figure on the left represents the empty map and the one on the right represents the one with the snake, where the numbers are the positions of each "piece" of the snake
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My second try on the Titanic problem

Titanic 2 - New try In [1]: % matplotlib inline import os import pandas as pd import matplotlib.pyplot as plt import numpy as np from sklearn.model_selection import train_test_split from sklearn.model_selection import StratifiedShuffleSplit from pandas.plotting import scatter_matrix import seaborn as sns from sklearn.impute import SimpleImputer from sklearn.preprocessing import OneHotEncoder from sklearn.base import BaseEstimator , TransformerMixin from sklearn.pipeline import Pipeline from sklearn.preprocessing import StandardScaler from sklearn.compose import ColumnTransformer from sklearn.linear_model import LogisticRegression from sklearn.tree import DecisionTreeRegressor from sklearn.ensemble import RandomForestRegressor from sklearn.metrics import mean_squared_error from sklearn.model_selection import cross_val_score from sklearn.model_selection