First of all, cut two 5" squares from 30 different novelty fabrics. Then cut 60 5" squares from your solid fabric. That requires 7 and a half 5" strips of standard-width fabric, so about 1.25 yards. I made binding out of the same solid, so add 1/2 yard more if you're planning to do the same.
Chain piece them all, keeping the pairs together. (If you're me, swear under your breath when you realize you only cut 14 strips when you "doubled the recipe", and then trudge back upstairs to cut one more strip - grrrr...)
When snipping the threads, separate the pairs into two piles, with one of each print in each pile. Then hand one pile to your house's randomizing unit. If you don't have a small child, maybe a few spins in the dryer on the fluff cycle would do?
While the randomizing is going on, take your first pile of 30 pairs and put 6 aside. Pair up the remaining 24 and sew them together to make 12 sets of 4, then pair those up and sew together to make 6 sets of 8, and then sew on the 6 you set aside, so that you end up with 6 sets of 10-square-long pieces. Iron those all in the same direction - I put the solid on the right and pressed the seams to the left.
Take those 6 rows, sew them together while alternating the orientation, to make a 6x10 checkerboard.
It will look something like this. Repeat the drill for the second randomized batch of pairs, except when it comes time to sew the rows together, take a moment to make sure that the row that will attach to the first half doesn't contain any of the same prints as that first row.
Sew the two halves together, iron the seams to one side, and you're done. Then take a digital picture and be amazed that somehow all the red blocks ended up on two rows. Oh well, truly random things have patterns, don't you know?
There you go, easy peasy!