Perdue University students tested this with a machine modeled after the human tongue. The machine reached the center in 364 licks. Students themselves gave it a try and the average was 252 licks.
University of Michigan students tested this with their own machine modeled after the human tongue as well. Their machine reached the center in 411 licks.
Swarthmore Junior High also tested this, using only their own tongues. The average was 144 licks to reach the center.
Therefore, the definitive answer depends on the tongue doing the licking!
Overall The World May Never Know