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_copy
    return merged_cards

split_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 cards

split_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_cards

shuffled_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_card

top_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 = 1
    elif region == "北":
        insert_count = 2
    else:
        insert_count = 3

    top = 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_cards


shuffled_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 = 0
    if gender == "男":
        take_count = 1
    elif gender == "女":
        take_count = 2
    else:
        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_cards

remaining_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 = 1
    while 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 += 1

    return 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_copy
    return merged_cards

split_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 cards

split_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_cards

shuffled_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_card

top_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 = 1
    elif region == "北":
        insert_count = 2
    else:
        insert_count = 3

    top = 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_cards


shuffled_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 = 0
    if gender == "男":
        take_count = 1
    elif gender == "女":
        take_count = 2
    else:
        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_cards


remaining_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 = 1
    while 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 += 1

    return 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。