who is fast in programming, try to make such an analysis.

for example rmd160 puzzle 66 like this

13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so 20d45a6a762535700ce9e0b216e31994335db8a5
0010000011010100010110100110101001110110001001010011010101110000000011001110100 1111000001011001000010110111000110001100110010100001100110101110110111000101001 01 160 len

"1" 73, "0" 87

according to this criterion

160!/73!/87!
50039953558241343191231898620403129563706328000

50039953558241343191231898620403129563706328000/2^65 1356335658972975302954605575

2^160/50039953558241343191231898620403129563706328000 29
2^65/29 1272189246462727697

2^65/2^20 35184372088832

2^160/2^65 39614081257132168796771975168
50039953558241343191231898620403129563706328000/39614081257132168796771975168  1263186017957493013   \
                                                                                           35184372088832×35968 1265511495291109376     > 2^60-2^61 
                                                                                                                 2^65/29 1272189246462727697   /

for every 1048576 step of puzzle 66, will fall around ~36000 "1" 73, "0" 87 and if we add fishing on the first 20 bits (for example)
001000001101010001011010011010100111011000100101001101010111000000001100111010011110000010110010000 1011011100011000110011001010000110011010111011011100010100101

then, based on the probability of dropping 20 bits, you need 1048576 outcomes

1048576/36000 29

1048576 × 30 31457280
1048576 × 29 30408704  there will be only 1 00100000110101000101 "1" 73, "0" 87
1048576 × 28 29360128

what is a full turn for example by 3

001
100
010

010
100
001

100
001
010

there may be such

100
100
001

001
001
001

etc

but in theory, when hashing, the data is simply shuffled, that is, rotated

this means that 20 bits (1048576  steps) in the first 00100000110101000101 will simply move to another place in the second (1048576  steps), third (1048576  steps), etc.

1048576×1048576 = 1099511627776 1 twist

2^65/1048576 = 35184372088832

35184372088832/1099511627776 32 twists for all puzzle 66


1048576×32 = 33554432 (there will be only 1 00100000110101000101 "1" 73, "0" 87)

2^65/33554432 = 1099511627776

all puzzle be

33554432 steps by 1099511627776 len or

1099511627776 steps by 33554432 len 

during the analysis, 1-3 drops out on such steps

we can rotate this space as we like, even take a square

6074001000
6074001000

imagine that we fill with zeros those addresses that do not suit us according to the sorting criterion and mark 1 those that do

we will get a similar picture

000001000001000100000000000000000001000000100000000000000001
001000000000000010000000000110000000000000000100000000100000
etc...

if we take another piece of 20 bits from the address, it will behave similarly

11011011100010100101

so these pieces will jump around the whole puzzle according to the random distribution and in total, as I wrote above, there will be 32 full turns

the idea is to take and randomly generate all possible collisions

select statistics from the puzzle space and try to jump by sorting the template


2^10*2^10                                                                        abbreviated example  2^65/33554432 = 1099511627776 (33554432  can be divided into 1024 parts)

001 010                                                                      000    <  000000000000000000000000000000000000001000000000000000000000000000  33554432 step
100 100                                                                      000    <  000000000000000000000000000000000000000000000000000000000000000001  33554432 step
010 001                                                                      000    <  000000000000000000000001000000000000000000000000000000000000000000  33554432 step