Created
December 16, 2012 21:27
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Find cycles of three six-sided dice such that each beats the next one with the same maximal probability; see http://math.stackexchange.com/questions/260072.
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public class Question260072 { | |
public static void main (String [] args) { | |
int [] [] dice = new int [3] [6]; | |
int [] counter = new int [3]; | |
int limit = (int) Math.pow (3,18); | |
int max = 0; | |
outer: | |
for (int selection = 0;selection < limit;selection++) { | |
// transform 18-digit ternary number into die sides | |
counter [0] = counter [1] = counter [2] = 0; | |
int n = selection; | |
for (int i = 0;i < 18;i++) { | |
int die = n % 3; | |
if (counter [die] == 6) | |
continue outer; | |
dice [die] [counter [die]++] = i; | |
n /= 3; | |
} | |
// determine winning probabilities | |
counter [0] = counter [1] = counter [2] = 0; | |
for (int i = 0;i < 3;i++) | |
for (int j = 0;j < 6;j++) | |
for (int k = 0;k < 6;k++) | |
if (dice [i] [j] > dice [(i + 1) % 3] [k]) | |
counter [i]++; | |
// are they all the same and maximal? | |
if (counter [0] >= max && counter [0] == counter [1] && counter [1] == counter [2]) { | |
max = counter [0]; | |
if (max == 21) { | |
// if this is an optimal set, print it only if the 0 is in the first set to avoid cyclic equivalents | |
boolean zeroHasZero = false; | |
for (int i = 0;i < 6;i++) | |
zeroHasZero |= dice [0] [i] == 0; | |
if (zeroHasZero) { | |
// collapse successive numbers on the same die into one | |
int lastDie = -1; | |
int lim = 18; | |
for (int i = 0;i < lim;) { | |
int die; | |
inner: | |
for (die = 0;die < 3;die++) | |
for (int k = 0;k < 6;k++) | |
if (dice [die] [k] == i) | |
break inner; | |
if (die == 4) | |
throw new Error (); | |
if (die == lastDie) { | |
for (int j = 0;j < 3;j++) | |
for (int k = 0;k < 6;k++) | |
if (dice [j] [k] >= i) | |
dice [j] [k]--; | |
lim--; | |
} | |
else { | |
lastDie = die; | |
i++; | |
} | |
} | |
// print the collapsed optimal set | |
for (int i = 0;i < 3;i++) { | |
System.out.print (" "); | |
for (int j = 0;j < 6;j++) | |
System.out.printf (" %d",dice [i] [j]); | |
System.out.println (); | |
} | |
System.out.println (); | |
} | |
} | |
} | |
} | |
System.out.println (max); | |
} | |
} |
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