Statues In the Garden

/**
* 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" );
}