There would be more than 24 sets each using 30 numbers. For example assume the following sets have 30 numbers in sequence ie an increase of 1 from one number to the next number in sequence.
{1...30}, {2...31} {3...32}, {4...33}, {5...34}, {6...35}, {7...36}, {8...37}, {9...38}, {10...39}, {11...40}, {12...41}, {13...42}, {14...43}, {15...44},
{16...45}, {17...46}, {18...47}, {19....48}, {20...49}
If you were to pick numbers 1,2,5,17,30,49 these numbers would not be covered by any of the above sets because 1 and 49 are not in the same set
That's 20 sets so far. Now add the following set which also has 30 numbers
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,31} - I have dropped number 30 and replaced it with 31. Only four numbers would match this set as 30 has been dropped and 49 is still not in this set.
If you keep removing and adding new numbers to create a new set you would end up with more than 24 sets in total.