All wallets in the puzzle were simply created randomly within their exponent.
There is no point in engaging in any type of hypothesis/study.
This is my opinion.
I totally agree, look at the % of the Range column
#puzzle Private Key Range Private Key
% of the Range-----------------------------------------------------------------------------------------
1 1...1 (2^0...2^1-1) 1 --> 100%
2 2...3 (2^1...2^2-1) 3 --> 100%
3 4...7 (2^2...2^3-1) 7 --> 100%
4 8...f (2^3...2^4-1) 8 --> 0%
5 10...1f (2^4...2^5-1) 15 --> 33.33%
6 20...3f (2^5...2^6-1) 31 --> 54.84%
7 40...7f (2^6...2^7-1) 4c --> 19.05%
8 80...ff (2^7...2^8-1) e0 --> 75.59%
9 100...1ff (2^8...2^9-1) 1d3 --> 82.75%
10 200...3ff (2^9...2^10-1) 202 --> 0.39%
11 400...7ff (2^10...2^11-1) 483 --> 12.81%
12 800...fff (2^11...2^12-1) a7b --> 31.02%
13 1000...1fff (2^12...2^13-1) 1460 --> 27.35%
14 2000...3fff (2^13...2^14-1) 2930 --> 28.71%
15 4000...7fff (2^14...2^15-1) 68f3 --> 63.99%
16 8000...ffff (2^15...2^16-1) c936 --> 57.2^%
17 10000...1ffff (2^16...2^17-1) 1764f --> 46.2^1%
18 20000...3ffff (2^17...2^18-1) 3080d --> 51.57%
19 40000...7ffff (2^18...2^19-1) 5749f --> 36.39%
20 80000...fffff (2^19...2^20-1) d2c55 --> 64.66%
21 100000...1fffff (2^20...2^21-1) 1ba534 --> 72.78%
22 200000...3fffff (2^21...2^22-1) 2de40f --> 43.41%
23 400000...7fffff (2^22...2^23-1) 556e52 --> 33.49%
24 800000...ffffff (2^23...2^24-1) dc2a04 --> 72%
25 1000000...1ffffff (2^24...2^25-1) 1fa5ee5 --> 97.8%
26 2000000...3ffffff (2^25...2^26-1) 340326e --> 62.54%
27 4000000...7ffffff (2^26...2^27-1) 6ac3875 --> 66.82%
28 8000000...fffffff (2^27...2^28-1) d916ce8 --> 69.6%
29 10000000...1fffffff (2^28...2^29-1) 17e2551e --> 49.2^8%
30 20000000...3fffffff (2^29...2^30-1) 3d94cd64 --> 92.44%
31 40000000...7fffffff (2^30...2^31-1) 7d4fe747 --> 95.8%
32 80000000...ffffffff (2^31...2^32-1) b862a62e --> 44.05%
33 100000000...1ffffffff (2^32...2^33-1) 1a96ca8d8 --> 66.18%
34 200000000...3ffffffff (2^33...2^34-1) 34a65911d --> 64.53%
35 400000000...7ffffffff (2^34...2^35-1) 4aed21170 --> 17.07%
36 800000000...fffffffff (2^35...2^36-1) 9de820a7c --> 23.36%
37 1000000000...1fffffffff (2^36...2^37-1) 1757756a93 --> 45.89%
38 2000000000...3fffffffff (2^37...2^38-1) 22382facd0 --> 6.94%
39 4000000000...7fffffffff (2^38...2^39-1) 4b5f8303e9 --> 17.77%
40 8000000000...ffffffffff (2^39...2^40-1) e9ae4933d6 --> 82.56%
41 10000000000...1ffffffffff (2^40...2^41-1) 153869acc5b --> 32.63%
42 20000000000...3ffffffffff (2^41...2^42-1) 2a221c58d8f --> 31.67%
43 40000000000...7ffffffffff (2^42...2^43-1) 6bd3b27c591 --> 68.48%
44 80000000000...fffffffffff (2^43...2^44-1) e02b35a358f --> 75.13%
45 100000000000...1fffffffffff (2^44...2^45-1) 122fca143c05 --> 13.67%
46 200000000000...3fffffffffff (2^45...2^46-1) 2ec18388d544 --> 46.11%
47 400000000000...7fffffffffff (2^46...2^47-1) 6cd610b53cba --> 70.06%
48 800000000000...ffffffffffff (2^47...2^48-1) ade6d7ce3b9b --> 35.86%
49 1000000000000...1ffffffffffff (2^48...2^49-1) 174176b015f4d --> 45.35%
50 2000000000000...3ffffffffffff (2^49...2^50-1) 22bd43c2e9354 --> 8.56%
51 4000000000000...7ffffffffffff (2^50...2^51-1) 75070a1a009d4 --> 82.86%
52 8000000000000...fffffffffffff (2^51...2^52-1) efae164cb9e3c --> 87.2^5%
53 10000000000000...1fffffffffffff (2^52...2^53-1) 180788e47e326c --> 50.18%
54 20000000000000...3fffffffffffff (2^53...2^54-1) 236fb6d5ad1f43 --> 10.74%
55 40000000000000...7fffffffffffff (2^54...2^55-1) 6abe1f9b67e114 --> 66.79%
56 80000000000000...ffffffffffffff (2^55...2^56-1) 9d18b63ac4ffdf --> 22.73%
57 100000000000000...1ffffffffffffff (2^56...2^57-1) 1eb25c90795d61c --> 91.85%
58 200000000000000...3ffffffffffffff (2^57...2^58-1) 2c675b852189a21 --> 38.76%
59 400000000000000...7ffffffffffffff (2^58...2^59-1) 7496cbb87cab44f --> 82.17%
60 800000000000000...fffffffffffffff (2^59...2^60-1) fc07a1825367bbe --> 96.9%
61 1000000000000000...1fffffffffffffff (2^60...2^61-1) 13c96a3742f64906 --> 23.67%
62 2000000000000000...3fffffffffffffff (2^61...2^62-1) 363d541eb611abee --> 69.5%
63 4000000000000000...7fffffffffffffff (2^62...2^63-1) 7cce5efdaccf6808 --> 95.01%
64 8000000000000000...ffffffffffffffff (2^63...2^64-1) f7051f27b09112d4 --> 92.98%
65 10000000000000000...1ffffffffffffffff (2^64...2^65-1)1a838b13505b26867 --> 65.71%