X16R algorithm intends to solve the ASIC mining problem by constantly disrupting the ordering of the hashing algorithms. The hashing algorithms are the same proven algorithms used in X15 + SHA512, but the ordering is changed based on the hash of the previous block. This reordering does not make an ASIC impossible to build, but it does require that the ASIC adapts to additional input, which is more easily accomplished by a CPU or GPU. The reordering also prevents a simple extension of the current X11 ASICs or future X15 ASICs.
