text: No, you cannot have 24 pairs of chromosomes even with mutations. Having XXXX does not give you 24 pairs of chromosomes; you still have 23 pairs with 4 chromosomes in pair #23. Your total number of chromosomes increases in that case to 48 instead of the normal number 46.\nMutations will either add or decrease the total number of chromosomes by either adding or deleting a chromosome to one pair. Notice that more than one chromosome could be added to a pair.\nDown's syndrome is caused by an extra chromosome to pair #21, resulting in 47 chromosomes with of course 23 pairs. Klinefelter's results in an extra X with also 23 pairs. The individual has 47 chromosomes; the 23rd pair or sex chromosomes is XXY.