Calculate the minimum and maximum values respectively.

In the smallest case, DE must be perpendicular to BC.

So: ∠ADE= 120, DA = DE ∠DAE = 30, ∠EAC = 30.

So: AE = 2*AC/ radical number 3 =2* radical number 3, DE = AE/ radical number 3 =2.

Maximum case: e must be infinitely close to b or c.

At this time, DA = DE, so d is the midpoint of AB, so DE = 3.

To sum up: 2