Statues In the Garden
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104
/**
* This is a rough program that simulates the working out of a logic problem
*
* The Premise of the Logic Problem as follows:-
*
* Two Prisoners are trapped in their individual cells,
* with no means of communicating with each other.
* Each of the prisoners can see through their cell window
* a number of status.
* Prisoner A sees 12 statues
* Prisoner B sees 8 statues
*
* Each day the Warden will ask the prisoners,
* in the same order,
* how many statues do the two prisonser see combined?
* 18 or 20 statues?
* If ONE of the prisoners answer correctly,
* BOTH prisoners will be released.
* If ONE of the prisoners ansers incorrectly,
* they will be imprisoned for the remainder of their lives.
* Prisoners may choose to answer or pass.
*
* How would the two Prisoners devise a means of arriving at the answer?
*
**/
var query = [18,20]; //The Question posed by the Warden
var min = null; // The collective implied minimum
var max = null; // The collective implied maximum
var minVisible = 12; //The number of statues Prisoner A sees
var maxVisible = 8; // The number of statues Prisoner B sees
var steps = 1; // The number of Days that has passed
/**
* Given a choice of two numbers,
* what are the complementary values to arrive at the two number
* given a target number
*
* Eg,
* given [18, 20]
* and a target number of 8
* the possible complementary values to arrive at 18 and 20 are
* [10, 12]
**/
function getPossibleValues(target, query ){
return query
.map(item=>item-target)
.filter(item=>item>=0);
}
/**
* Prisoner A's deductive logic and implying the Minimum Value
**/
function minimize( query, min, max, visible ){
min = min || 0;
console.log( "Maximize : " );
console.log( getPossibleValues(min,query));
return Math.min.apply(null,getPossibleValues(min,query));
}
/**
* Prisoner B's deductive logic and implying the Maximum Value
**/
function maximize( query, min, max ){
console.log( "Maximize :");
min = min || 0;
var valueFilter = item=>item<=max;
for( var i = min; i <= max; i++ ){1
var possibleValues = getPossibleValues(i,query).filter(valueFilter);
console.log(i, "=>", possibleValues);
if( possibleValues.length > 1 ){
console.log( "First Number with no definite solutions : ", i, " => ", possibleValues );
return i;
}
}
return null;
}
/**
* Simulates the daily routine where the Warden asks the Prisoners
**/
function step(){
console.log("Day ", steps );
max = minimize(query, min, max, minVisible);
min = maximize(query, min, max, maxVisible);
console.log("Min : ", min, "; Max : ", max, "; MinVisible : ", minVisible, "; MaxVisible : ", maxVisible );
steps++;
}
/**
* Run the simulation until a solution is reached
**/
do{
step();
} while( min !== maxVisible && max !== minVisible || steps >= 1000 );
if( steps < 1000 ){
console.log( "Day " + steps++ );
console.log( "Prisoner arrives at the answer ", min+max );
} else {
console.log( 1000, " days has passed - both prisoners have given up" );
}
JavaScript
INFO