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import numpy as np

#  Compute expected number of turns to complete a snakes & ladders
#  track of length n, given a set of portals (snakes and ladders),
#  which are both represented as lists of pairs (start, end).
#  It's ok to pass lists of [start, end] instead of pairs (start, end).

def E(n, portals):
    portal_map = {k: k for k in range(n)}     # identity map
    portal_map.update(portals)

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• is
• this
• markdown

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#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <string.h>
#include <time.h>

typedef uint8_t byte;
typedef uint32_t quart;
typedef uint64_t pottle;

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from fractions import Fraction
from functools import lru_cache
from itertools import *

def powerset(S):
    return chain.from_iterable(combinations(S, r) for r in range(len(S)+1))

@lru_cache(maxsize=512)
def p(S):                     #  S is a frozenset so it can be cached
    if len(S) == 0:

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	PAGE	58,132

;----------------------------------------------------------------------------
;  Hier sind der neu SETUP komputerprogramm.
;----------------------------------------------------------------------------

	.386P

FALSE	EQU	0

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import random

N = 2018
trials = 10000

def connect(wires):
    loops = 0
    while wires > 1:
        v, w = random.randrange(wires), random.randrange(wires)
        if v == w:

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# Determine how many ways the US election could end in electoral tie.
# Respsonse to https://twitter.com/daveinstpaul/status/792788962230226944

from functools import lru_cache

votes = [9,8,3,3,8,18,11,4,7,6,10,7,55,11,20,9,16,4,7,10,9,3,6,3,3,10,
         11,29,3,38,16,5,6,4,6,3,4,4,13,20,14,12,11,5,5,6,29,10,6,15,3]

@lru_cache(maxsize=10000)
def count_ties(subtotal, votes):

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import matplotlib.pyplot as plt
from pylab import savefig
import numpy as np
from numpy.random import rand, randint

def flipsome(n):
	flip = lambda: randint(0,2)
	return sum(flip() for _ in range(n)) / float(n)

interval = 1000

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digits = [

#          B C                  D           A B C             A B C   
#        E     F                F                 F                 F 
#        G     H                H                 H                 H 
#        I     L                L             J K               J K   
#        M     N                N           M                       N 
#        O     P                P           O                       P 
#          R S                  T           Q R S T           Q R S   

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from math import sqrt
from itertools import permutations

def squarable(sides):
	area = sum(map(lambda (a,b): a*b, sides))
	S = sqrt(area)
	if S == int(S):

		# check Ken's conditions