Yes! However, in reality, there are very few. The eight characters are composed of 22 characters of heavenly stems and earthly branches, which belong to the five elements of fire, water and earth in Jin Mu. Just like you buy lottery tickets, it is impossible to choose the same number, and the probability is too low.
The so-called purity means that the eight characters are a single five elements. Such as: Jia Yin Jia Yin Jia Yin Jia Yin Jia Yin
Heavenly stems and earthly branches is all wood (for the sun)
Yi Mao Mao Yi Mao Yi Mao Yi
Heavenly stems and earthly branches is full of wood (for shade)