There are two kinds of triangles in this problem. One is a triangle with a circle on each vertex and a circle on each side of the vertex, with three * * *; Two, a triangle consisting of a circle in the middle and two circles on one side, three * * *;

Nine circles of three triangles on the vertex and 10 circles in the middle are not duplicated. The three triangles on the vertex require the sum of three circles of each triangle to be equal, so the sum of nine circles of the three triangles on the vertex can be divisible by 3. Because 45 is divisible by 3, the possible middle numbers are 0, 3, 6 and 9.

Fill 0 in the middle, and the sum of the three triangles on the vertex is (45-0)/3= 15. The sum of the middle number and the numbers on both sides should be 15, and the sum of the numbers on both sides should be 15-0= 15, that is, 1.

Fill 3 in the middle, and the sum of the three triangles on the vertex is (45-3)/3= 14. The sum of the middle number and the numbers on both sides should be 14, and the sum of the numbers on both sides should be 14-3= 1 1, that is, 0. The numbers of the three triangles on the vertex are: 0+5+9= 14, 1+6+7= 14, 8+2+4 =14;

Fill 6 in the middle, and the sum of the three triangles on the vertex is (45-6)/3= 13. The sum of the middle number and the numbers on both sides should be 13, and the sum of the numbers on both sides should be 13-6=7. 3 out of 0-5 and 7-9. The numbers filled in by the three triangles on the vertex are: 1+5+7= 13, 8+2+3= 13, 9+0+4 =13;

Fill 9 in the middle, and the sum of the three triangles on the vertex is (45-9)/3= 12. The sum of the middle number and the numbers on both sides should be 12, and the sum of the numbers on both sides should be 12-9=3. 0-8, only 1.