3. (8 points) Place the numbers $1-8$ at the eight vertices of a cube, then write the average of the numbers at the two endpoints of each edge at the midpoint of that edge. If the numbers written at the midpoints of the four edges of the top face and the four edges of the bottom face are all integers, then among the numbers written at the other four midpoints, there are $\qquad$ that are not integers.
【Answer】Solution: For the odd-even problem, among the numbers $1 \sim 8$, there are 4 odd and 4 even numbers. To satisfy the condition that the sum of adjacent numbers is even in both the upper and lower groups of 4 numbers, the only scenario is that the numbers in each group are either all odd or all even. That is, the upper 4 numbers are all odd and the lower 4 numbers are all even, or the upper 4 numbers are all even and the lower 4 numbers are all odd.

Therefore, the sum of the 4 groups of numbers in the upper and lower rows are all odd, meaning their averages are not integers.
So there are 4 averages that are not integers.
The answer is 4.