To produce a normal zygote how many chromosomes would each sperm and egg have

The answer should be each has 23 chromosomes. 

The normal somatic (body) cells in human should have 46 chromosomes, which is also 2 complete set. All the cells in our body should have 46 chromosomes each (unless other rare cases), however, except our gametes (cells for reproduction, sperms/eggs). This is because, in fertilization, a sperm and an egg will fuse together to produce a zygote, if both sperm and egg have a chromosome number of 46, the zygote would have doubled chromosomes, which is impossible. 

So, in order to help restore the correct number of chromosomes in zygotes/offsprings, the gametes only have half of the chromosomes (23 in human) comparing to other somatic cells such as bone cells or skin cells. These cells with only half of the chromosomes can be called haploid cells, and they're usually produced by a cell division process called meiosis.