const int buttonPin = 2;
const int ledPin = 13;

int buttonPushCounter = 0;
int buttonState = 0;
int lastButtonState = 0;

void setup() {
  pinMode(buttonPin, INPUT);
  pinMode(ledPin, OUTPUT);
  Serial.begin(9600);
}

void loop() {
  buttonState = digitalRead(buttonPin);

  if (buttonState != lastButtonState) {
    if (buttonState == HIGH) {
      buttonPushCounter++;
      Serial.println("on");
      Serial.print("number of button pushes: ");
      Serial.println(buttonPushCounter);
    } else {
      Serial.println("off");
    }
    delay(50);
  }
  lastButtonState = buttonState;

  if (buttonPushCounter % 4 == 0) {
    digitalWrite(ledPin, HIGH);
  } else {
    digitalWrite(ledPin, LOW);
  }
}