Can anyone help me with Hardy-Weinberg problems?

If a population is at Hardy-Weinberg equilibrium, then the allele frequency does not change.  So, if q = 0.1 and the population is at Hardy-Weinberg equilibrium, then after 100 generations, q will still be equal to 0.1

Hardy-Weinberg problems are based on the idea that the sum of the frequencies of two alleles for a gene is equal to 1.  Put another way, if one allele frequency is 0.1, then the other allele frequency must be equal to 0.9:

0.1 + 0.9 = 1

If it helps, you can think of it in percentages, so that if q = 0.1, this is the same as saying 10% of the alleles of a single gene are q and so since there is only one other possible allele (p) for this gene, then these other alleles are 90% of the possible alleles for the gene, such that the total is 100%.

The Hardy-Weinberg equation comes from this idea of allele frequencies adding up to 1 (p + q = 1) by simply squaring both sides of the equation.  If p is the frequency of one allele and q the frequency of the other allele for the gene of interest, then:

p + q = 1
(p + q)^2 = 1^2
p^2 + 2pq + q^2 = 1

where p^2 is the frequency of one homozygote in the population, 2pq is the frequency of the heterozygote and q^2 is the frequency of the other homozygote in the population.  This formula works because if you understand statistics, you'll realize that the probability of having two events occur simultaneously is the product of the probabilities of each event.  This means that if the allele frequency for q is 0.1, then the probability of having 2 q alleles q x q = q^2 = 0.1 x 0.1 = 0.01

For Hardy-Weinberg to be absolutely true and the allele frequencies to be absolutely true and unchanging for generations, then the allele frequencies cannot change between generations (I know that sounds redundant), which means that there cannot be any gene flow into or out of the population, no mutations, no genetic variation of any kind and the population must be large so that there is no genetic drift.  This is an ideal situation which is unlikely to be encountered in the real world.  However, the formula can work well in most situations because the ideal situation doesn't have to exist for the formula to work in most cases.  Mathematicians hate that we can't give them an ideal situation all the time, but hey, that's biology!

Good luck!