14. Let's consider any 4 segments, which do not have common extremity-circles (they are marked in the fig. 1. The total number of extremities of those segments is 6 + 10 + 10 + 10 = 36, therefore the 9-th number, not included in this sum equals to (1 + 2 + ... + 9) - 36=9. Then in the shaded circle we'll write 9. Now, at once, we can fill in the remaining circles (fig. 2), the same way.
Fig. 1	Fig. 2