The person who created the puzzle has already posted exactly how he did it.
Not exactly. He just mentioned that values are random. But randomness can be very different.
If you look at the table with keys 1-55 you'll see that keys
tend to sit in second part of range.
Unless and until they don't. The selection of key is totally random within the range with all values equally likely. Seeing or creating "trends" in random data is a very human thing to do but unfortunately for your theory the private keys for each range were created by having a
computer create a 256 bit secure random number and then masking the result down to the desired key length.
If you search the top half of the range for any key there is exactly a 50% chance of the key being in the top half of the range.