Can we reach Nirvana without removing ignorance? Namo Buddhaya.
I am learning dependent origination.

If we follow the dependent origination strictly then by cutting off craving , the attachment ceases to be and with cessation of attachment, continuation ceases to be and with cessation of continuation , birth ceases to be and with cessation of birth , the suffering ceases to be. As the suffering ceases, Nirvana is attained.

In the above sequence of happenings we do not need to mention Ignorance. However we know that dependent origination begins with Ignorance. 

My question is : can we reach to Nirvana ,without removing ignorance and just by cutting off craving ? Or is cutting off of the craving is same as removing the ignorance?
Maybe you've heard of the old South Indian Monkey Trap (from this article):


  In Zen And The Art Of Motorcycle Maintenance, Robert Pirsig’s
  bonkers-but-brilliant philosophical novel that turns 40 this year, he
  describes “the old South Indian Monkey Trap”. ... The trap
  “consists of a hollowed-out coconut, chained to a stake. The coconut
  has some rice inside which can be grabbed through a small hole”. The
  monkey’s hand fits through the hole, but his clenched fist can’t fit
  back out. “The monkey is suddenly trapped.” But not by anything
  physical. He’s trapped by an idea, unable to see that a principle that
  served him well – “when you see rice, hold on tight!” – has become
  lethal.


The monkey needs to let go of the rice in order to free himself from his suffering. The way to end his suffering, is to end his craving for rice.

But in order to end his craving for rice, he must first understand how his hand is stuck inside the coconut. When the monkey overcomes his ignorance about how the trap works, he would let go of his craving for rice, and release his clenched fist. With this, he would be free from his suffering.

Also you can say that the monkey's suffering originated with his ignorance of the trap.


(Illustration above: Paul Thurlby for the Guardian)