integrating a homemade captcha to sign up and sign in?

Question

So I have a basic sign up, sign in site with username and password. I don't want to use recaptcha and was wondering whether i can create my own? So have for example 'what colour is an orange'.

I was wondering how you could integrate this (if you can that is) into the form_for as it wouldn't be part of the @user object and throws an error.

Here is the controller

def new
 @user = User.new
 @captcha = Captcha.find(rand(1..3))
end

def create
 @user = User.new(user_params)
 if @user.save
  session[:user_id] = @user.id
  redirect_to root_path
 else
  render 'new'
 end
end

private

def user_params
 params.require(:user).permit(:username, :password, :release_pin)
end

Here is the view

    <div class="sign-in-form">
      <%= form_for @user do |form| %>
        <div class="form-text">
          <%= form.label :username %> <br>
          <%= form.text_field :username %>
        </div>
        <br>
        <div class="form-text">
          <%= form.label :password %> <br>
          <%= form.text_field :password %>
        </div>
        <br>

     ############## this here obviously throws 
     an error but this is the kind of thing i would want #########


        <div class="form-text">
          <p> <%[email protected]%> </p>   
          <%= form.text_field :captcha_answer %>
        </div>

        <div class="form-text">
          <%= form.submit "Submit" %>
        </div>

I've looked into nested forms but don't think that's the correct answer... but I could wrong as I'm only a beginner. thanks