Shuffle deck of cards without built-in random functon - math

Question

My friend suggested me to try to solve this problem before interview, but I have no idea on how to approach it.
I need to write a code to shuffle a deck of 52 cards without using a built-in standard random function.
Update
Thanks to Yifei Wu, his answer was very helpful.
Here is a link for my github project where I executed the given algorithm
https://github.com/Dantsj16/Shuffle-Without-Random.git

Answer 1

Your question does not say it must be a random shuffle of 52 cards. There is such a thing as a perfect shuffle, where a riffle shuffle is done with the top card remaining on the top and every other card comes from the other half of the deck. Many magicians and card sharks can do this shuffle as desired. It is well known that eight perfect shuffles in a row of a standard 52-card deck returns the cards to their original order, if the top card remains on top for each shuffle.
Here are 8 perfect shuffles in python Note that this shuffle is done differently than an actual manual shuffle would be done, to simplify the code.
In [1]: d0=[x for x in range(1,53)] # the card deck
In [2]: print(d0)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52]
In [3]: d1=d0[::2]+d0[1::2] # a perfect shuffle
In [4]: print(d1)
[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52]
In [5]: d2=d1[::2]+d1[1::2]
In [6]: d3=d2[::2]+d2[1::2]
In [7]: d4=d3[::2]+d3[1::2]
In [8]: d5=d4[::2]+d4[1::2]
In [9]: d6=d5[::2]+d5[1::2]
In [10]: d7=d6[::2]+d6[1::2]
In [11]: d8=d7[::2]+d7[1::2]
In [12]: print(d8)
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52]
In [13]: print(d0 == d8)
True
If you want the perfect shuffle as done by hand, use
d1=[None]*52
d1[::2]=d0[:26]
d1[1::2]=d0[26:]
This gives, for d1,
[1, 27, 2, 28, 3, 29, 4, 30, 5, 31, 6, 32, 7, 33, 8, 34, 9, 35, 10, 36, 11, 37, 12, 38, 13, 39, 14, 40, 15, 41, 16, 42, 17, 43, 18, 44, 19, 45, 20, 46, 21, 47, 22, 48, 23, 49, 24, 50, 25, 51, 26, 52]
Let me know if you really need a random shuffle. I can adapt my Borland Delphi code into python if you need it.