Multiple push buttons
Your code won't work as is. Each time you assign a value to state you're overwriting it in the next line. You could, for example have multiple int state variables such as state1 for the first line in the loop then state2 in the second etc. Then you need to compare values (don't use = on its own in a compare as it will assign the value being tested - use == instead). This way you gather all the button states first.

Or you could test the state of a button and if pressed add 1 to state:

if (digitalRead(bp1)) {
    state++};


Then you compare the number of button presses counted in state as you were doing and light the LEDs based on that.

However you will likely have a problem with contact bounce on the switches. This happens when a switch is closing and the voltage is not steady for about 20ms (imaging a switch sparking as it is closing). To get around this you'll need either some additional components or add a time delay in your code for each button press to check it several times until the voltage is stable. Do a Google search for 'Arduino contact bounce' for solutions.

R3.