In order to figure this one out you have to write equations describing the problem.
If we let n=number of nickels, d=number of dimes and q=number of quarters then
we must have .05n+.1d+.25q=1.0 and n,d,q must be non negative integers and further 0≤q≤4
Now if you put q=0 in the above equation and solve for n you get n=20-2d now let d=0,1,2.....10 that makes 11 different combinations of nickels and dimes and 0 quarters that add up to one dollar. Repeat for q=1,2,3,4 and add up all the solutions. I got 29.
There probably is a more elegant way to solve this problem, this is the brute force method.
Hope this helps.