Finding an intermediate value between two variables

The logic I noticed is as follows:

When a - c = 7 , then a and c could have values:

a   c       b
----------------
9   2 --> a - 3 |
10  3 --> a - 3 | --> qualquer "a" dividido por 4 resulta em par (descartando as decimais)
11  4 --> a - 3 |

13  6 --> a - 4 |
14  7 --> a - 4 | --> qualquer "a" dividido por 4 resulta em ímpar (descartando as decimais)
15  8 --> a - 4 |
...
31  24 --> a - 4

For each group of 3 values of a , the value of b can be a - 3 or a - 4 . Also note if I divide each value from a to 4 , I will have a logical sequence of each group with odd or even result of 3 in 3 numbers .

So,% w / w% would be:

var b = ~~(a/4)%2 == 0 ? a - 3 : a - 4;

In the case of b , the same logic applies to the value of a - c = 9 instead of c of the previous case:

a   c       b
----------------
10  1 --> a - 4 |
11  2 --> a - 4 | --> qualquer "c" dividido por 4 resulta em par (descartando as decimais)
12  3 --> a - 4 |

14  5 --> a - 5 |
15  6 --> a - 5 | --> qualquer "c" dividido por 4 resulta em ímpar (descartando as decimais)
16  7 --> a - 5 |
...
32 23 --> a - 5

Logo:

var b = ~~(c/4)%2 == 0 ? a - 4 : a - 5;

Example:

var a = 13,
    c = 6;

if (a - c == 7){
   
   var b = ~~(a/4)%2 == 0 ? a - 3 : a - 4;
   
   if (a - 3 == b){
      console.log("b igual a-3");
   } else
   if (a - 4 == b){
      console.log("b igual a-4");
   }
} else
if (a - c == 9){

   var b = ~~(c/4)%2 == 0 ? a - 4 : a - 5;

   if (a - 4 == b){
      console.log("b igual a-4");
   } else
   if (a - 5 == b){
      console.log("b igual a-5");
   }
}

console.log("b = "+b);

You can use the calculaB function below:

• This function receives the two numbers a and c and then chooses the two values in the middle that can be b .

• These values are obtained by calculating the average between a and c , where one of them is the mean rounded down and the other is the average rounded up.

• If both values match, only one is returned. If they do not match, both are returned, the first being smaller.

function calculaB(a, c) {
    var media = (c + a) / 2;
    var b1 = Math.floor(media);
    var b2 = Math.ceil(media);
    return b1 === b2 ? [b1] : [b1, b2];
}

$("#calcular").click(function() {
    var a = parseInt($("#a").val());
    var c = parseInt($("#c").val());
    var bs = calculaB(a, c);
    $("#b").val(bs);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script><div><labelfor="a">a:</label><input type="text" id="a" value="" /></div>
<div><label for="c">c:</label><input type="text" id="c" value="" /></div>
<div><button id="calcular">Calcular</button></div>
<div><label for="b">b:</label><input type="text" id="b" value="" readonly="true" /></div>

Click the blue "Run" button to test the above code.

First, let's imagine that the board had all 64 numbered houses instead of just the 32 dark ones. For this we need a function that converts its numbering format to a numbering format with the 64 houses. Here is this function:

function recalcula32to64(casa) {
    return casa * 2 - (Math.floor((casa - 1) / 4) % 2 === 0 ? 0 : 1);
}

And also a function that does the inverse:

function recalcula64to32(casa) {
    return casa % 2 === 0 ? casa / 2 : (casa + 1) / 2;
}

And then just figure out which is the middle house:

function calculaB(a, c) {
    return recalcula64to32((recalcula32to64(a) + recalcula32to64(c)) / 2);
}

function recalcula32to64(casa) {
    return casa * 2 - (Math.floor((casa - 1) / 4) % 2 === 0 ? 0 : 1);
}

function recalcula64to32(casa) {
    return casa % 2 === 0 ? casa / 2 : (casa + 1) / 2;
}

function calculaB(a, c) {
    return recalcula64to32((recalcula32to64(a) + recalcula32to64(c)) / 2);
}

$("#calcular").click(function() {
    var a = parseInt($("#a").val());
    var c = parseInt($("#c").val());
    var bs = calculaB(a, c);
    $("#b").val(bs);
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script><div><labelfor="a">a:</label><input type="text" id="a" value="" /></div>
<div><label for="c">c:</label><input type="text" id="c" value="" /></div>
<div><button id="calcular">Calcular</button></div>
<div><label for="b">b:</label><input type="text" id="b" value="" readonly="true" /></div>

Click the blue "Run" button to test the above code.