Mainly Tech projects on Python and Electronic Design Automation.

Friday, February 05, 2016

Mind boggling card trick in Python


A Python version of the Mind boggling card trick.


Get a pack of 52 cards, half red - half black. (You might need to find those missing cards from that old pack)
In [61]:
n = 52
Black, Red = 'Black', 'Red'
blacks = [Black] * (n // 2) 
reds = [Red] * (n // 2)
pack = blacks + reds

Shuffle the pack!

Give the pack a good shuffle. (Don't drop any).
In [62]:
import random
random.shuffle(pack)

Deal those random cards

  1. Assemble the cards face down.
  2. Turn up the top card, if it is black then add the next card, unseen, to the black-stack. If it is red then instead add that next card, unseen, to the red-stack.
  3. Add the card you turned over to see what colour it was above to the discard stack.
  4. Repeat the above for the whole pack.
In [63]:
black_stack, red_stack, discard = [], [], []
while pack:
    top = pack.pop()
    print(top[0], end=' ')
    if top == Black:
        black_stack.append(pack.pop())
    else:
        red_stack.append(pack.pop())
    discard.append(top)
print()
            
R B R R B R R R B B B B B B B B R R B B B R R R R R 
There is still randomness present. The discard stack shown above seems pretty random.

Swap the same, random, number of cards between the two stacks.

We can't swap more than the number of cards in a stack.
In [64]:
max_swaps = min(len(black_stack), len(red_stack))
Randomly choose the number of cards to swap. (You could use a dice).
In [65]:
swap_count = random.randint(0, max_swaps)
print('Swapping', swap_count)
Swapping 11
Randomly choose that number of cards out of each stack to swap. (Without knowing those cards - they could be red or black cards from the stacks, we don't know)
In [66]:
def random_partition(stack, count):
    "Partition the stack into 'count' randomly selected members and the rest"
    sample = random.sample(stack, count)
    rest = stack[::]
    for card in sample:
        rest.remove(card)
    return rest, sample

black_stack, black_swap = random_partition(black_stack, swap_count)
red_stack, red_swap = random_partition(red_stack, swap_count)
Perform the swap.
In [67]:
black_stack += red_swap
red_stack += black_swap

Order from randomness?

The mathematician asserts that:
  • The number of black cards in the black pile equals the number of red cards in the red pile
In [68]:
if black_stack.count(Black) == red_stack.count(Red):
    print('Yea! The mathematician is right.')
else:
    print('Woops - That mathematician (or my card manipulations) are flakey')
Yea! The mathematician is right.

2 comments:

  1. "If it is red then instead add that next card, unseen, to the black-stack."
    Shouldn’t it read "red-stack"?

    ReplyDelete
    Replies
    1. Well caught,! Now fixed.

      Thanks Martin :-)

      Delete

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