Algorithm for guessing letters of a name won't display certain letters and gets stuck between (I and R). How can I improve my algorithm?

Question

The algorithm is suppose to ask the middle letter of the English alphabet, in my program its N. At this point it asks the user whether:

1. The guess is correct

2. The letter is earlier in the alphabet.

3. The letter is later in the alphabet

When trying to guess Jose, it will first ask about N. I choose option 2 which then gives me G. I then choose option 3 which then gives me Q. I then choose option 2 which then gives me I. I then choose option 3 which then gives me R. If I choose option 2, it gives me R again, and basically I'm stuck between R and I. How can I fix my algorithm to properly provide all letters available?

My code is the following:

int let = 26/2;
if(n != 0) {
    //Correct guess
    if(n == 3) {
        aLetter = alphabet[let];
        actualLetter = Character.toString(aLetter);
        aName.add(actualLetter);
    }
    //earlier in alphabetical order
    else if(n == 2) {
        let /= 2;
    }
    //later in alphabetical order
    else if(n == 1) {
        for(int i = let; i < 27; i++){
            r += 1;
        }
        r /= 2;
        let += r;
       r=0;
    }

} //done guessing
else if (n == 0) {
    for(String str: aName) {
        result3 += str;
    }
}

Any help and or advice would be great. Thanks!

Answer 1

Problem 1

Say the letter of the alphabet (represented by --- etc.) being guessed is "s" (represented by +). The computer will first guess in the middle (let = 13, represented by |).

-------------|---+--------

You tell the computer to guess higher.

With the code

for(int i = let; i < 27; i++) {
    r += 1;
}
r /= 2;
let += r;
r=0;

which can be shortened to

let += (26 - let) / 2;

the computer will guess halfway to the end (let = 19):

-------------|---+-|------

So far so good.

Now, you tell it to guess lower. The computer knows it's higher than 13 and lower than 19, so it should guess halfway in between. However, the code you have does not do that.

let /= 2;

makes let be (int)(19 / 2), i.e., 9.

---------|---|---+-|------

What you want is let = 16

-------------|--|-+|------

Problem 2

Let's say you successfully got to

-------------|--|-+|------

with the most recent guess being 16. You tell the computer to guess higher. With the code

let += (26 - let) / 2;

let will become 21.

-------------|--|-+|-|----

What you want is let = 18 or 19;

Solution

In general, a good algorithm should make let go up or down by "13 / 2ⁿ" each iteration, where "n" is the iteration number (starting at 0).

You should therefore use the code

int let = 0;
int iteration = 0;

//start loop
//take input

int delta = 13 / Math.pow(2, iteration) + 1;

if(n != 0) {
    //if n == 3
    else if(n == 2)
    {
        let -= delta;
    }
    else if(n == 1)
    {
        let += delta;
    }
}
iteration++;
//end loop

and replace the comments with the code you are already using.