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简介
这是新春的第一篇，今天早上睡到了自然醒，打开手机刷视频就被刘谦的魔术所吸引，忍不住用编程去模拟一下这个过程。
首先，声明的一点，大年初一不学习，所以这其中涉及的数学原理约瑟夫环大家可以找找其他的教程看看，我这块只是复现它魔术里面的每个步骤。
魔术的步骤
总而言之，可以分为以下8个步骤：
Step 1: 将四张4张牌撕成两半，直接将两堆叠放;
Step 2: 假设姓名为n个字，重复n次，将堆在最上的牌放到最下面；
Step 3: 将牌堆最上的3张拿出，不改变顺序，并随机插入牌堆中间；
Step 4: 将牌堆最上方的牌拿走，放在一旁；
Step 5: 按照南/北/不知道是南或者北方地区，判断自己属于哪一地区，并分别将牌堆最上的1/2/3，不改变顺序，并随机插入牌堆中间;
Step 6: 按性别男/女，从牌堆最上方拿走1/2张牌，一边念口诀：“见证奇迹的时刻”，每念一个字，将牌堆最上方的牌放到牌堆最下;
Step 7: 念口诀“好运留下米”时，将牌堆最上的牌放到牌堆最下；念“烦恼扔出去”时，将牌堆最上方的牌移除。重复这两句口诀，直到手中只有一张牌；
Step 8: 最后留下的牌和Step 4拿走的牌是一样的。
过程拆开分来其实就是对列表进行一个简单的操作了
用python实现其中的过程
0. 模拟扑克牌打乱并抽取的过程;
import random
import itertools
import copy
# 定义扑克牌
suits = ['红桃', '方块', '梅花', '黑桃']
ranks = ['A', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K']
jokers = ['小王', '大王']
deck_of_cards = list(itertools.product(suits, ranks)) + jokers
random.shuffle(deck_of_cards) # 模拟打乱的操作
print(f"随机生成的{len(deck_of_cards)}扑克牌:", deck_of_cards)
selected_cards = random.sample(deck_of_cards, 4)
print("随机抽取其中的四张牌:", selected_cards)随机抽取其中的四张牌: [('红桃', '9'), ('黑桃', '8'), ('黑桃', 'A'), ('黑桃', 'K')]
1. 将四张4张牌撕成两半，直接将两堆叠放;
def split_and_stack(cards):cards_copy = copy.copy(cards)merged_cards = cards + cards_copyreturn merged_cardssplit_cards = split_and_stack(selected_cards)
print("撕成两半后堆叠:", split_cards)撕成两半后堆叠: [('红桃', '9'), ('黑桃', '8'), ('黑桃', 'A'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', '8'), ('黑桃', 'A'), ('黑桃', 'K')]
2. 假设姓名为n个字，重复n次，将堆在最上的牌放到最下面；
def repeat_name(cards, name):name_length = len(name)for _ in range(name_length):# 取出堆在最上的牌,放到最下面top_card = cards.pop(0) cards.append(top_card) return cardssplit_cards_repeated = repeat_name(split_cards, name)
print(f"{name} 重复姓名字数次后的牌堆:", split_cards_repeated)
夏天是冰红茶 重复姓名字数次后的牌堆: [('黑桃', 'A'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', '8'), ('黑桃', 'A'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', '8')]
3. 将牌堆最上的3张拿出，不改变顺序，并随机插入牌堆中间；
def take_top_and_insert(cards):top_three_cards = cards[:3] # 取出最上面的3张牌remaining_cards = cards[3:] # 剩下的牌insert_index = random.randint(1, len(remaining_cards))shuffled_cards = remaining_cards[:insert_index] + top_three_cards + remaining_cards[insert_index:]return shuffled_cardsshuffled_cards = take_top_and_insert(split_cards_repeated)
print("牌堆最上的3张拿出，随机插入后的牌堆:", shuffled_cards)
牌堆最上的3张拿出，随机插入后的牌堆: [('黑桃', '8'), ('黑桃', 'A'), ('黑桃', 'A'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', '8')]
4. 将牌堆最上方的牌拿走，放在一旁；
def take_top_card(cards):top_card = cards.pop(0) # 取出最上方的牌return top_cardtop_card = take_top_card(shuffled_cards)
print("拿走的牌:", top_card)
print("剩余的牌:", shuffled_cards)拿走的牌: ('黑桃', '8')
剩余的牌: [('黑桃', 'A'), ('黑桃', 'A'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', '8')]
5. 按照南/北/不知道是南或者北方地区，判断自己属于哪一地区，并分别将牌堆最上的1/2/3，不改变顺序，并随机插入牌堆中间;
def insert_cards_based_on_region(cards, region):if region == "南":insert_count = 1elif region == "北":insert_count = 2else:insert_count = 3top = cards[:insert_count]remaining_cards = cards[insert_count:]insert_index = random.randint(0, len(remaining_cards)-1)shuffled_cards = remaining_cards[:insert_index] + top + remaining_cards[insert_index:]return shuffled_cardsshuffled_cards_region = insert_cards_based_on_region(shuffled_cards, region)
print(f"{region}方地区插入后的牌堆:", shuffled_cards_region)
南方地区插入后的牌堆: [('黑桃', 'A'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'K'), ('黑桃', 'A'), ('红桃', '9'), ('黑桃', '8')]
6. 按性别男/女，从牌堆最上方拿走1/2张牌，一边念口诀：“见证奇迹的时刻”，每念一个字，将牌堆最上方的牌放到牌堆最下;
def take_and_chant(cards, gender, chant="见证奇迹的时刻"):take_count = 0if gender == "男":take_count = 1elif gender == "女":take_count = 2else:print("未知性别")remaining_cards = cards[take_count:] # 剩下的牌print(remaining_cards)# 念口诀过程for c in chant:remaining_cards.append(remaining_cards.pop(0)) # 将最上方的牌放到牌堆最下return remaining_cardsremaining_cards= take_and_chant(shuffled_cards_region, gender, chant)
print(f"剩余的牌堆:", remaining_cards)[('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'K'), ('黑桃', 'A'), ('红桃', '9'), ('黑桃', '8')]
剩余的牌堆: [('红桃', '9'), ('黑桃', 'K'), ('黑桃', 'A'), ('红桃', '9'), ('黑桃', '8'), ('黑桃', 'K')]
7/8. 念口诀“好运留下米”时，将牌堆最上的牌放到牌堆最下；念“烦恼扔出去”时，将牌堆最上方的牌移除。重复这两句口诀，直到手中只有一张牌；最后留下的牌和Step 4拿走的牌是一样的。
def chant_and_modify(cards):iter = 1while len(cards) > 1:chant_good_luck = "好运留下米"chant_throw_away = "烦恼扔出去"print(f"\n第{iter}轮口诀开始:")cards.append(cards.pop(0))print(f"口诀{chant_good_luck}结束后手上的牌:", cards)cards.pop(0)print(f"口诀{chant_throw_away}结束后手上的牌:", cards)iter += 1return cards[0]final_card = chant_and_modify(remaining_cards)
print(f"\n最终留下的牌:{final_card}, Step 4:{top_card}")第1轮口诀开始:
口诀好运留下米结束后手上的牌: [('黑桃', 'K'), ('黑桃', 'A'), ('红桃', '9'), ('黑桃', '8'), ('黑桃', 'K'), ('红桃', '9')]
口诀烦恼扔出去结束后手上的牌: [('黑桃', 'A'), ('红桃', '9'), ('黑桃', '8'), ('黑桃', 'K'), ('红桃', '9')]
第2轮口诀开始:
口诀好运留下米结束后手上的牌: [('红桃', '9'), ('黑桃', '8'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'A')]
口诀烦恼扔出去结束后手上的牌: [('黑桃', '8'), ('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'A')]
第3轮口诀开始:
口诀好运留下米结束后手上的牌: [('黑桃', 'K'), ('红桃', '9'), ('黑桃', 'A'), ('黑桃', '8')]
口诀烦恼扔出去结束后手上的牌: [('红桃', '9'), ('黑桃', 'A'), ('黑桃', '8')]
第4轮口诀开始:
口诀好运留下米结束后手上的牌: [('黑桃', 'A'), ('黑桃', '8'), ('红桃', '9')]
口诀烦恼扔出去结束后手上的牌: [('黑桃', '8'), ('红桃', '9')]
第5轮口诀开始:
口诀好运留下米结束后手上的牌: [('红桃', '9'), ('黑桃', '8')]
口诀烦恼扔出去结束后手上的牌: [('黑桃', '8')]
最终留下的牌:('黑桃', '8'), Step 4:('黑桃', '8')
完整的代码
import random
import itertools
import copy
# 定义扑克牌
suits = ['红桃', '方块', '梅花', '黑桃']
ranks = ['A', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K']
jokers = ['小王', '大王']
deck_of_cards = list(itertools.product(suits, ranks)) + jokers
random.shuffle(deck_of_cards) # 模拟打乱的操作
print(f"随机生成的{len(deck_of_cards)}扑克牌:", deck_of_cards)
selected_cards = random.sample(deck_of_cards, 4)
print("随机抽取其中的四张牌:", selected_cards)# 模拟性别为男的情况
name = "夏天是冰红茶"
gender = "男"
chant = "见证奇迹的时刻"
region = "南"# step 1: 将四张4张牌撕成两半，直接将两堆叠放;
def split_and_stack(cards):cards_copy = copy.copy(cards)merged_cards = cards + cards_copyreturn merged_cardssplit_cards = split_and_stack(selected_cards)
print("撕成两半后堆叠:", split_cards)# Step 2: 设你的姓名为n个字，重复n次，将堆在最上的牌放到最下面；
def repeat_name(cards, name):name_length = len(name)for _ in range(name_length):# 取出堆在最上的牌,放到最下面top_card = cards.pop(0)cards.append(top_card)return cardssplit_cards_repeated = repeat_name(split_cards, name)
print(f"{name} 重复姓名字数次后的牌堆:", split_cards_repeated)# Step 3: 将牌堆最上的3张拿出，不改变顺序，并随机插入牌堆中间
def take_top_and_insert(cards):top_three_cards = cards[:3] # 取出最上面的3张牌remaining_cards = cards[3:] # 剩下的牌insert_index = random.randint(1, len(remaining_cards))shuffled_cards = remaining_cards[:insert_index] + top_three_cards + remaining_cards[insert_index:]return shuffled_cardsshuffled_cards = take_top_and_insert(split_cards_repeated)
print("牌堆最上的3张拿出，随机插入后的牌堆:", shuffled_cards)# Step 4: 将牌堆最上方的牌拿走，放在一旁
def take_top_card(cards):top_card = cards.pop(0) # 取出最上方的牌return top_cardtop_card = take_top_card(shuffled_cards)
print("拿走的牌:", top_card)
print("剩余的牌:", shuffled_cards)# Step 5: 按照南/北/不知道是南或者北方地区，判断自己属于哪一地区，并分别将牌堆最上的1/2/3，不改变顺序，并随机插入牌堆中间
def insert_cards_based_on_region(cards, region):if region == "南":insert_count = 1elif region == "北":insert_count = 2else:insert_count = 3top = cards[:insert_count]remaining_cards = cards[insert_count:]insert_index = random.randint(0, len(remaining_cards)-1)shuffled_cards = remaining_cards[:insert_index] + top + remaining_cards[insert_index:]return shuffled_cardsshuffled_cards_region = insert_cards_based_on_region(shuffled_cards, region)
print(f"{region}方地区插入后的牌堆:", shuffled_cards_region)# Step 6: 按性别男/女，从牌堆最上方拿走1/2张牌，一边念口诀：“见证奇迹的时刻”，每念一个字，将牌堆最上方的牌放到牌堆最下。
def take_and_chant(cards, gender, chant="见证奇迹的时刻"):take_count = 0if gender == "男":take_count = 1elif gender == "女":take_count = 2else:print("未知性别")remaining_cards = cards[take_count:] # 剩下的牌print(remaining_cards)# 念口诀过程for c in chant:remaining_cards.append(remaining_cards.pop(0)) # 将最上方的牌放到牌堆最下return remaining_cardsremaining_cards= take_and_chant(shuffled_cards_region, gender, chant)
print(f"剩余的牌堆:", remaining_cards)# Step 7: 念口诀“好运留下米”时，将牌堆最上的牌放到牌堆最下；念“烦恼扔出去”时，将牌堆最上方的牌移除。重复这两句口诀，直到手中只有一张牌；
def chant_and_modify(cards):iter = 1while len(cards) > 1:chant_good_luck = "好运留下米"chant_throw_away = "烦恼扔出去"print(f"\n第{iter}轮口诀开始:")cards.append(cards.pop(0))print(f"口诀{chant_good_luck}结束后手上的牌:", cards)cards.pop(0)print(f"口诀{chant_throw_away}结束后手上的牌:", cards)iter += 1return cards[0]# Step 8: 最后留下的牌和Step 4拿走的牌是一样的。
final_card = chant_and_modify(remaining_cards)
print(f"\n最终留下的牌:{final_card}, Step 4:{top_card}")
大家可以自己去试一试，在步骤6后男生拿走的牌总是会在对应的第5位，女生拿走的牌总是会在对应的第3位。
结语
其实说实话，这种数学魔术在我小时候买的书里就曾经看到过许多。虽然现在了解了其中的数学原理，但当时的惊奇与欢乐感觉依然难以忘怀。刘谦老师在表演中展现了非凡的技艺，不仅仅是数学的巧妙运用，更是他善于抓住观众的好奇心，创造出让人难以置信的奇迹。
