Need help making a Pointless Scoreboard with React.js

Ok. So I want to make a Pointless Scoreboard application for a friend who is holding a quiz. For you who dont know, Pointless is the name of a gameshow. Here is a clip of what I'm trying to achieve (https://www.youtube.com/watch?v=cmdAQHzNYF8). Right, so I have my App-component which looks like this

import React, { Component } from 'react';
import Countdown from './components/Countdown';
import StartCountdownForm from './components/StartCountdownForm';

import './App.css';

class App extends Component {

  state = {
    points: [],
    score: 100,
    targetScore: 0,
  };

  componentWillMount() {
    let p = [];
    for (let i = 0; i < 100; i++) {
      p.push(<div className="point"></div>);
    }
    this.setState({
      points: p
    });
  }
  removeTopPoint () {
    var tmp = this.state.points; 
    tmp.splice(0, 1);
    this.setState( prevState => ({
      score: prevState.score -= 1,
      poins: tmp
    }));
  }

  render() {
    return (
      <div className="pointless-container">
        <Countdown score={this.state.score} />
          <div className="points-container">
          { this.state.points.map( (point, index) =>
            <div className="point"
              key={index}></div>
            )}
          </div>
          <StartCountdownForm />
      </div>
    );
  }
}

export default App;

Ok, so first of all; I don't quite know how to properly initiate my points-array. I tried initiating it in state (with like points: new Array(100)), but I couldn't make it work. The way I see it it would suffice to just have an array with 100 places, but I might be wrong and I welcome alternative ways for implementing it. As of now Im using the componentWillMount-function to fill the array and then I loop through it to print out the same div each time. Yes, I know it's retarded, but I don't know how to properly do it. So that's the first thing. Secondly, I want it to be possible for the user to enter a target score for the countdown to stop at. I wrote the function removeTopPoint(), which kinda works. So I'm thinking it should be possible to call this function over and over again until I reach the target score with the help of something like setInterval(). But I'm struggling to make it work. The closest I got made the countdown stop at the target score, but all the points where removed at the same time. I want them to disappear one by one. I might also want to add a class to each point first, before I remove it, so that I can make a similar effect as in the show. I haven't included the Countdown-component or the StartCountdownForm-component here, as they really dont have any logic written in them as of now. Hope someone can help! I would really appreciate it.