Based and inspired by 3Blue1Brown's Pi Collisions Video.

piCollisions.cpp

// Includes
#include <iostream>

class Box {
 private:
  long double x, v, m, w;

 public:
  Box(long double wx, long double mx) {
    w = wx;
    m = mx;
  };
  Box() = default;
  Box(Box &b) = default;
  Box(Box &&b) = default;

  void place(long double xx) { x = xx; }
  void setVel(long double vx) { v = vx; }
  void move() { x += v; }
  void reverse() { v *= -1; }
  bool hitByLeftWall(long double xx) { return (x <= xx); }
  bool hitByRightWall(long double xx) { return (x + w >= xx); }
  bool collideByLeft(const Box &b) { return !(x + w < b.x); }
  bool collideByRight(const Box &b) { return !(x > b.x + b.w); }
  bool impossible(const Box &b) { return (v > 0 && b.v > 0 && b.v > v); }
  friend void bounce(Box &, Box &);
};

void bounce(Box &a, Box &b) {
  long double v1 = a.v;
  long double v2 = b.v;
  long double sum = a.m + b.m;
  b.v = (2 * a.m * v1 + (b.m - a.m) * v2) / sum;
  a.v = (2 * b.m * v2 + (a.m - b.m) * v1) / sum;
}

long double powTimesTen(int x) {
  long double res = 1.00;
  long double p = 10.00;
  while (x > 0) {
    if (x & 1) {
      res *= p;
    }
    p *= p;
    x /= 2;
  }
  return res;
}

long double powByTen(int x) {
  long double res = 1.00;
  long double p = 10.00;
  while (x > 0) {
    if (x & 1) {
      res /= p;
    }
    p *= p;
    x /= 2;
  }
  return res;
}

int main() {
  const long double leftWall = 0;
  const long double rightWall = 1e18;
  long long count = 0;
  int times;

  // digits
  std::cin >> times;

  Box block1 = Box(10.00, powByTen(times));
  Box block2 = Box(10.00, powTimesTen(times));
  block1.place(20.00);
  block1.setVel(0.00);
  block2.place(40.00);
  block2.setVel(-1.00 * powByTen(times));

  while (!block1.impossible(block2)) {
    block1.move();
    block2.move();
    if (block1.collideByLeft(block2)) {
      bounce(block1, block2);
      count++;
    }
    if (block1.hitByLeftWall(leftWall)) {
      block1.reverse();
      count++;
    }
  }

  std::cout << count;
}