4. There are dozens of holes (less than 100) on a circle, as shown in the figure. Xiao Ming, like playing checkers, starts from hole A and jumps in a counterclockwise direction, skipping a certain number of holes each step, hoping to return to hole A after one full circle. He first tries to jump by skipping 2 holes each step, but he only lands on hole B. Then he tries to jump by skipping 4 holes each step, and he still only lands on hole B. Finally, he jumps by skipping 6 holes each step and successfully returns to hole A. Do you know how many holes are on this circle?
91
4.【Solution】Imagine the holes on the circle are numbered as follows: Hole A is numbered 1, and then the holes are numbered sequentially in a counterclockwise direction as $2,3,4, \cdots$ until Hole B, which is the total number of holes on the circle. If you jump every 2 holes, you land on $1,4,7,10, \cdots$. Finally, you land on Hole B, so the total number of holes is a multiple of 3 plus 1. Similarly, if you jump every 4 holes and finally land on Hole B, it means the total number of holes is a multiple of 5 plus 1; and if you jump every 6 holes and finally return to Hole A, it means the total number of holes is a multiple of 7.

If you subtract 1 from the total number of holes, the result is both a multiple of 3 and a multiple of 5, and thus a multiple of 15. This multiple of 15 plus 1 equals the total number of holes, and it must also be divisible by 7. Note that 15 divided by 7 leaves a remainder of 1, so $15 \times 6$ divided by 7 leaves a remainder of 6, and $15 \times 6 + 1$ is exactly divisible by 7. We can also see that adding 1 to any other multiple of 15 (less than 7) does not result in a number divisible by 7, and $15 \times 7 = 105$ is already greater than 100. Multiples of 7 and above do not need to be considered, so the total number of holes on the circle is $15 \times 6 + 1 = 91$.

Answer: There are 91 holes on the circle.