How to resolve the algorithm Mind boggling card trick step by step in the XPL0 programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Mind boggling card trick step by step in the XPL0 programming language
Table of Contents
Problem Statement
Matt Parker of the "Stand Up Maths channel" has a YouTube video of a card trick that creates a semblance of order from chaos. The task is to simulate the trick in a way that mimics the steps shown in the video.
(Optionally, run this simulation a number of times, gathering more evidence of the truthfulness of the assertion.) Show output on this page.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Mind boggling card trick step by step in the XPL0 programming language
Source code in the xpl0 programming language
include xpllib; \for Print
char Deck(52), BlackPile(52), RedPile(52), DiscardPile(52),
BlackBunch(52), RedBunch(52);
int I, J, T, M, X, Y, BP, RP, DP, BB, RB, BC, RC;
proc Show;
[Print("Black pile: ");
for I:= 0 to BP-1 do ChOut(0, BlackPile(I));
Print("\nRed pile: ");
for I:= 0 to RP-1 do ChOut(0, RedPile(I));
Print("\nDiscard pile: ");
for I:= 0 to DP-1 do ChOut(0, DiscardPile(I));
Print("\n");
];
[for I:= 0 to 26-1 do
[Deck(I):= ^r; Deck(I+26):= ^b];
for I:= 0 to 52-1 do
[Y:= Ran(52); \0..51
T:= Deck(I); Deck(I):= Deck(Y); Deck(Y):= T;
];
BP:= 0; RP:= 0; DP:= 0;
for I:= 0 to 52-1 do
[if Deck(I) = ^b then
[BlackPile(BP):= Deck(I+1); BP:= BP+1]
else
[RedPile (RP):= Deck(I+1); RP:= RP+1];
DiscardPile(DP):= Deck(I); DP:= DP+1;
I:= I+1;
];
Show;
M:= BP;
if RP < M then M:= RP;
X:= Ran(M) + 1;
Print("Swap %d cards between the red and black piles.\n", X);
RB:= 0; BB:= 0;
for I:= 0 to X-1 do
[repeat Y:= Ran(RP); until RedPile(Y) # 0;
RedBunch(RB):= RedPile(Y); RB:= RB+1; RedPile(Y):= 0;
];
for I:= 0 to X-1 do
[repeat Y:= Ran(BP); until BlackPile(Y) # 0;
BlackBunch(BB):= BlackPile(Y); BB:= BB+1; BlackPile(Y):= 0;
];
RB:= 0;
for I:= 0 to X-1 do
[J:= 0;
while BlackPile(J) # 0 do J:= J+1;
BlackPile(J):= RedBunch(RB); RB:= RB+1;
];
BB:= 0;
for I:= 0 to X-1 do
[J:= 0;
while RedPile(J) # 0 do J:= J+1;
RedPile(J):= BlackBunch(BB); BB:= BB+1;
];
Show;
BC:= 0;
for I:= 0 to BP-1 do
if BlackPile(I) = ^b then BC:= BC+1;
RC:= 0;
for I:= 0 to RP-1 do
if RedPile(I) = ^r then RC:= RC+1;
Print("The number of black cards in the black pile is %d.\n", BC);
Print("The number of red cards in the red pile is %d.\n", RC);
Print("The mathematician's assertion is%s correct.\n",
if BC#RC then " not" else "");
]
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