The sum of the total times all the hats were seen is 1+2+3+4+5+6+7+8=36 times, so the number of times each color hat was seen is 12. There are three hats in each color. Because no one can see the last child's hat, only two hats with the same color as the last child's hat can be seen, while three hats with other two colors should be seen. So the numbers that make up 12 are 3, 3 and 2 respectively.

It is known that the third place has a red hat, and the number of times it has been seen is 6, so the other two red hats must have been seen. Because if the last child wears a red hat, the other red hat must be watched six times to meet the condition that the total number of times is 12, which is obviously impossible. In other words, the last child didn't wear a red hat.

The sixth one has a yellow hat and has been seen 3 times. To satisfy the condition that the total number of times is 12, the total number of times the other two yellow hats are seen must be 9. As can be seen from the above, the number of times a hat in any position is seen is 9, so the other two yellow hats must be seen, which means that 9 is the sum of the number of times the other two yellow hats are seen. Then the last one is not wearing a yellow hat.

To sum up, the last child is wearing a blue hat.