Wikipedia:Reference desk/Archives/Mathematics/2017 November 16

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November 16

Any logical sequence for this...

One wants to find out certain numbers between 123456 and 654321. The numbers should be all :

1. Not containg any digit above 6
2. No digit should occur more than once. (for example 154236 is OK, but not 154266)

What number should be added (which will be a different number each time. For example, since first "next" number will be 123465, which we'll get by adding 9, but next one will be gotten by adding 81, which will be 123546).

But how to get the next one satisfying above two conditions ?  Jon Ascton  (talk) 05:51, 16 November 2017 (UTC)

• XY problem alert: I suspect what you are actually looking for is a way to enumerate permutations, so that you do not really care about storing them as integers.

[1] has some algorithms. [2] gives a few implementations in Python. Some of them enumerate in lexicographic order (= increasing order when the permutations are stored as the digits of a number). Tigraan^{Click here to contact me} 09:40, 16 November 2017 (UTC)

Is the digit 0 allowed? If not, there should be 6!=720 numbers which meet the condition. If yes, there should be 7!-1=5039 (in both cases including the boundary numbers). --Stephan Schulz (talk) 09:45, 16 November 2017 (UTC)

No, I'm afraid 0 isn't allowed. Of course, the number of numbers we'll get will be 6!. Yeah, boundary numbers, both 123456 and 654321 will be part of the numbers selected, smallest and biggest respectively. Both meet the conditions: no digit of no digit being <1 or >6, or digit-repeted. Kindly elaborate if you see a problem there:  Jon Ascton  (talk) 11:20, 16 November 2017 (UTC)

For Tigraan: OK, pal, let's revise it (in hope that it won't be an XY problem anymore). Say the problem is all:-

One wants to find out certain numbers between 123456 and 654321. Each of numbers should :

1. Not contain any digit above 6
2. No digit should occur more than once. (for example 154236 is OK, but not 154266)
3. None should have 0 in it.

What number should be added (which will be a different number each time. What number should be added (which will be a different number each time. For example, since first "next" number will be 123465, which we'll get by adding 9, but next one will be gotten by adding 81, which will be 123546)  Jon Ascton  (talk) 11:20, 16 November 2017 (UTC)

• Yawn. Well, this does not look like a homework problem, and it is simple enough that I can just blurt out the solution, I guess. The following Python script solves the problem:

import itertools
def tuple_into_num(l):
    N=len(l)
    res=0
    for i in range(N):
        res += l[i]*10**(N-1-i)
    return res


gen=itertools.permutations([1,2,3,4,5,6])
for item in gen:
   print(tuple_into_num(item))

Resulting blob:

All permutations of [1,2,3,4,5,6] (in integer form)

123456 123465 123546 123564 123645 123654 124356 124365 124536 124563 124635 124653 125346 125364 125436 125463 125634 125643 126345 126354 126435 126453 126534 126543 132456 132465 132546 132564 132645 132654 134256 134265 134526 134562 134625 134652 135246 135264 135426 135462 135624 135642 136245 136254 136425 136452 136524 136542 142356 142365 142536 142563 142635 142653 143256 143265 143526 143562 143625 143652 145236 145263 145326 145362 145623 145632 146235 146253 146325 146352 146523 146532 152346 152364 152436 152463 152634 152643 153246 153264 153426 153462 153624 153642 154236 154263 154326 154362 154623 154632 156234 156243 156324 156342 156423 156432 162345 162354 162435 162453 162534 162543 163245 163254 163425 163452 163524 163542 164235 164253 164325 164352 164523 164532 165234 165243 165324 165342 165423 165432 213456 213465 213546 213564 213645 213654 214356 214365 214536 214563 214635 214653 215346 215364 215436 215463 215634 215643 216345 216354 216435 216453 216534 216543 231456 231465 231546 231564 231645 231654 234156 234165 234516 234561 234615 234651 235146 235164 235416 235461 235614 235641 236145 236154 236415 236451 236514 236541 241356 241365 241536 241563 241635 241653 243156 243165 243516 243561 243615 243651 245136 245163 245316 245361 245613 245631 246135 246153 246315 246351 246513 246531 251346 251364 251436 251463 251634 251643 253146 253164 253416 253461 253614 253641 254136 254163 254316 254361 254613 254631 256134 256143 256314 256341 256413 256431 261345 261354 261435 261453 261534 261543 263145 263154 263415 263451 263514 263541 264135 264153 264315 264351 264513 264531 265134 265143 265314 265341 265413 265431 312456 312465 312546 312564 312645 312654 314256 314265 314526 314562 314625 314652 315246 315264 315426 315462 315624 315642 316245 316254 316425 316452 316524 316542 321456 321465 321546 321564 321645 321654 324156 324165 324516 324561 324615 324651 325146 325164 325416 325461 325614 325641 326145 326154 326415 326451 326514 326541 341256 341265 341526 341562 341625 341652 342156 342165 342516 342561 342615 342651 345126 345162 345216 345261 345612 345621 346125 346152 346215 346251 346512 346521 351246 351264 351426 351462 351624 351642 352146 352164 352416 352461 352614 352641 354126 354162 354216 354261 354612 354621 356124 356142 356214 356241 356412 356421 361245 361254 361425 361452 361524 361542 362145 362154 362415 362451 362514 362541 364125 364152 364215 364251 364512 364521 365124 365142 365214 365241 365412 365421 412356 412365 412536 412563 412635 412653 413256 413265 413526 413562 413625 413652 415236 415263 415326 415362 415623 415632 416235 416253 416325 416352 416523 416532 421356 421365 421536 421563 421635 421653 423156 423165 423516 423561 423615 423651 425136 425163 425316 425361 425613 425631 426135 426153 426315 426351 426513 426531 431256 431265 431526 431562 431625 431652 432156 432165 432516 432561 432615 432651 435126 435162 435216 435261 435612 435621 436125 436152 436215 436251 436512 436521 451236 451263 451326 451362 451623 451632 452136 452163 452316 452361 452613 452631 453126 453162 453216 453261 453612 453621 456123 456132 456213 456231 456312 456321 461235 461253 461325 461352 461523 461532 462135 462153 462315 462351 462513 462531 463125 463152 463215 463251 463512 463521 465123 465132 465213 465231 465312 465321 512346 512364 512436 512463 512634 512643 513246 513264 513426 513462 513624 513642 514236 514263 514326 514362 514623 514632 516234 516243 516324 516342 516423 516432 521346 521364 521436 521463 521634 521643 523146 523164 523416 523461 523614 523641 524136 524163 524316 524361 524613 524631 526134 526143 526314 526341 526413 526431 531246 531264 531426 531462 531624 531642 532146 532164 532416 532461 532614 532641 534126 534162 534216 534261 534612 534621 536124 536142 536214 536241 536412 536421 541236 541263 541326 541362 541623 541632 542136 542163 542316 542361 542613 542631 543126 543162 543216 543261 543612 543621 546123 546132 546213 546231 546312 546321 561234 561243 561324 561342 561423 561432 562134 562143 562314 562341 562413 562431 563124 563142 563214 563241 563412 563421 564123 564132 564213 564231 564312 564321 612345 612354 612435 612453 612534 612543 613245 613254 613425 613452 613524 613542 614235 614253 614325 614352 614523 614532 615234 615243 615324 615342 615423 615432 621345 621354 621435 621453 621534 621543 623145 623154 623415 623451 623514 623541 624135 624153 624315 624351 624513 624531 625134 625143 625314 625341 625413 625431 631245 631254 631425 631452 631524 631542 632145 632154 632415 632451 632514 632541 634125 634152 634215 634251 634512 634521 635124 635142 635214 635241 635412 635421 641235 641253 641325 641352 641523 641532 642135 642153 642315 642351 642513 642531 643125 643152 643215 643251 643512 643521 645123 645132 645213 645231 645312 645321 651234 651243 651324 651342 651423 651432 652134 652143 652314 652341 652413 652431 653124 653142 653214 653241 653412 653421 654123 654132 654213 654231 654312 654321

Tigraan^{Click here to contact me} 12:52, 16 November 2017 (UTC)

Wonderful ! You got all those numbers by writing so small a coding ! And if I tried it using VB6 (my obsession) I had to write at least 20 times if not more than that. Guess, must learn this blackmagic called Python... Jon Ascton  (talk) 14:01, 16 November 2017 (UTC)

Tigraan is being so verbose. This also works:

import itertools
gen=itertools.permutations([1,2,3,4,5,6])
for line in gen:
   print("".join([str(item) for item in line]))

Dragons flight (talk) 14:45, 16 November 2017 (UTC)

Maybe I'm too anal, but that last line should be

    print(int("".join([str(item) for item in line])))

.

The OP asked for numbers, not strings that happen to be decimal representations of numbers ;-). --Stephan Schulz (talk) 15:31, 16 November 2017 (UTC)

How can we give him a number instead of some form of representation of that number? I feel that I am in the border between mathematics and philosophy! -- Q Chris (talk) 15:47, 16 November 2017 (UTC)

Well, as long as the number is printed, the difference is philosophical. But assuming the OP wants to do something with the numbers inside the program, the type matters. In Python, a string and an int have different types with different properties, and, more importantly, different operations. --Stephan Schulz (talk) 16:15, 16 November 2017 (UTC)

Well, I would have written a shorter script but I did not have the time. I would probably have taken more time finding how to avoid the t-uple to int routine than it took writing it. And even inside it, I was pretty sure when writing the for loop than there was a more Pythonic option but did not care - for the interested reader: the untested return sum(l[i]*10**(N-1-i) for i in range(N)) is a good candidate.

On the "philosophical" issue of what type to return, I saw a relevant comment something like five years ago on http://thedailywtf.com/ to the effect that "if you are not adding or multiplying them, they are not really numbers"; meaning a program should not use integers to store data that is not meant for arithmetics. Exhibit #1 was a front end display of a "phone number" field as "1.5579E10" or similar; a phone number is functionally a string, even if it is a string of digits.

Here, we cannot read OP's mind and they did not tell what they are going to use the "integers" for, but the problem screams that those are permutations, not numbers, so the natural representation is probably an array/list. In those optics a string (= array of characters) is better than an int output (and worse than a list/t-uple output in Python). Tigraan^{Click here to contact me} 17:36, 16 November 2017 (UTC)

You miss one important point. The OP was asking for numbers. So we should give him numbers. We don't know if he wants or needs numbers, but we should always follow rule number one of practical project management: The most important goal is not to succeed, but to make sure that the finger of blame is pointing in the right direction (i.e. away from you ;-). --Stephan Schulz (talk) 07:58, 17 November 2017 (UTC)

The OP asked also "what number should be added each time", i.e. to get each permutation from the one before (though they deleted that bit further down the dialogue). As a matter of interest, if the permutations are put in ascending order, is there any obvious pattern to these successive differences? →217.43.234.32 (talk) 10:25, 17 November 2017 (UTC)

I hand-hacked a script for the differences, and there are some regularities, but nothing obvious. I then entered the first few terms into the On-Line Encyclopedia of Integer Sequences and it came back with sequence A219664, which basically is a generalised form of the differences of the permutations sequence and has no particularly interesting properties listed. The original series, however, is at A178476, and that one has a link to A178475 (the same thing with digits 1-5), which lists a relatively efficient procedure for computing the nth element. BTW, I suspect it's a symptom of terminal nerd if you click around OEIS in the same way you click around Wikipedia... --Stephan Schulz (talk) 11:53, 17 November 2017 (UTC)

Since the difference of any two permutations of a number given in base b is a multiple of b-1, it is reasonable to divide these first differences by 9 when seeking patterns. This yields OEIS: A217626, with interesting notes in the comments section. -- ToE 18:39, 20 November 2017 (UTC)

So I made this program to take hte differences:

Code
z = [] for yz in range(123456, 654322): if sorted(str(yz)) == sorted(str(123456)): z.append(yz) for n in range(0, 719): y = int(z[n+1]) - int(z[n]) print "The difference of", z[n+1], "and", z[n], "is", y

It gave me this output:

The aoutput

The difference of 123465 and 123456 is 9 The difference of 123546 and 123465 is 81 The difference of 123564 and 123546 is 18 The difference of 123645 and 123564 is 81 The difference of 123654 and 123645 is 9 The difference of 124356 and 123654 is 702 The difference of 124365 and 124356 is 9 The difference of 124536 and 124365 is 171 The difference of 124563 and 124536 is 27 The difference of 124635 and 124563 is 72 The difference of 124653 and 124635 is 18 The difference of 125346 and 124653 is 693 The difference of 125364 and 125346 is 18 The difference of 125436 and 125364 is 72 The difference of 125463 and 125436 is 27 The difference of 125634 and 125463 is 171 The difference of 125643 and 125634 is 9 The difference of 126345 and 125643 is 702 The difference of 126354 and 126345 is 9 The difference of 126435 and 126354 is 81 The difference of 126453 and 126435 is 18 The difference of 126534 and 126453 is 81 The difference of 126543 and 126534 is 9 The difference of 132456 and 126543 is 5913 The difference of 132465 and 132456 is 9 The difference of 132546 and 132465 is 81 The difference of 132564 and 132546 is 18 The difference of 132645 and 132564 is 81 The difference of 132654 and 132645 is 9 The difference of 134256 and 132654 is 1602 The difference of 134265 and 134256 is 9 The difference of 134526 and 134265 is 261 The difference of 134562 and 134526 is 36 The difference of 134625 and 134562 is 63 The difference of 134652 and 134625 is 27 The difference of 135246 and 134652 is 594 The difference of 135264 and 135246 is 18 The difference of 135426 and 135264 is 162 The difference of 135462 and 135426 is 36 The difference of 135624 and 135462 is 162 The difference of 135642 and 135624 is 18 The difference of 136245 and 135642 is 603 The difference of 136254 and 136245 is 9 The difference of 136425 and 136254 is 171 The difference of 136452 and 136425 is 27 The difference of 136524 and 136452 is 72 The difference of 136542 and 136524 is 18 The difference of 142356 and 136542 is 5814 The difference of 142365 and 142356 is 9 The difference of 142536 and 142365 is 171 The difference of 142563 and 142536 is 27 The difference of 142635 and 142563 is 72 The difference of 142653 and 142635 is 18 The difference of 143256 and 142653 is 603 The difference of 143265 and 143256 is 9 The difference of 143526 and 143265 is 261 The difference of 143562 and 143526 is 36 The difference of 143625 and 143562 is 63 The difference of 143652 and 143625 is 27 The difference of 145236 and 143652 is 1584 The difference of 145263 and 145236 is 27 The difference of 145326 and 145263 is 63 The difference of 145362 and 145326 is 36 The difference of 145623 and 145362 is 261 The difference of 145632 and 145623 is 9 The difference of 146235 and 145632 is 603 The difference of 146253 and 146235 is 18 The difference of 146325 and 146253 is 72 The difference of 146352 and 146325 is 27 The difference of 146523 and 146352 is 171 The difference of 146532 and 146523 is 9 The difference of 152346 and 146532 is 5814 The difference of 152364 and 152346 is 18 The difference of 152436 and 152364 is 72 The difference of 152463 and 152436 is 27 The difference of 152634 and 152463 is 171 The difference of 152643 and 152634 is 9 The difference of 153246 and 152643 is 603 The difference of 153264 and 153246 is 18 The difference of 153426 and 153264 is 162 The difference of 153462 and 153426 is 36 The difference of 153624 and 153462 is 162 The difference of 153642 and 153624 is 18 The difference of 154236 and 153642 is 594 The difference of 154263 and 154236 is 27 The difference of 154326 and 154263 is 63 The difference of 154362 and 154326 is 36 The difference of 154623 and 154362 is 261 The difference of 154632 and 154623 is 9 The difference of 156234 and 154632 is 1602 The difference of 156243 and 156234 is 9 The difference of 156324 and 156243 is 81 The difference of 156342 and 156324 is 18 The difference of 156423 and 156342 is 81 The difference of 156432 and 156423 is 9 The difference of 162345 and 156432 is 5913 The difference of 162354 and 162345 is 9 The difference of 162435 and 162354 is 81 The difference of 162453 and 162435 is 18 The difference of 162534 and 162453 is 81 The difference of 162543 and 162534 is 9 The difference of 163245 and 162543 is 702 The difference of 163254 and 163245 is 9 The difference of 163425 and 163254 is 171 The difference of 163452 and 163425 is 27 The difference of 163524 and 163452 is 72 The difference of 163542 and 163524 is 18 The difference of 164235 and 163542 is 693 The difference of 164253 and 164235 is 18 The difference of 164325 and 164253 is 72 The difference of 164352 and 164325 is 27 The difference of 164523 and 164352 is 171 The difference of 164532 and 164523 is 9 The difference of 165234 and 164532 is 702 The difference of 165243 and 165234 is 9 The difference of 165324 and 165243 is 81 The difference of 165342 and 165324 is 18 The difference of 165423 and 165342 is 81 The difference of 165432 and 165423 is 9 The difference of 213456 and 165432 is 48024 The difference of 213465 and 213456 is 9 The difference of 213546 and 213465 is 81 The difference of 213564 and 213546 is 18 The difference of 213645 and 213564 is 81 The difference of 213654 and 213645 is 9 The difference of 214356 and 213654 is 702 The difference of 214365 and 214356 is 9 The difference of 214536 and 214365 is 171 The difference of 214563 and 214536 is 27 The difference of 214635 and 214563 is 72 The difference of 214653 and 214635 is 18 The difference of 215346 and 214653 is 693 The difference of 215364 and 215346 is 18 The difference of 215436 and 215364 is 72 The difference of 215463 and 215436 is 27 The difference of 215634 and 215463 is 171 The difference of 215643 and 215634 is 9 The difference of 216345 and 215643 is 702 The difference of 216354 and 216345 is 9 The difference of 216435 and 216354 is 81 The difference of 216453 and 216435 is 18 The difference of 216534 and 216453 is 81 The difference of 216543 and 216534 is 9 The difference of 231456 and 216543 is 14913 The difference of 231465 and 231456 is 9 The difference of 231546 and 231465 is 81 The difference of 231564 and 231546 is 18 The difference of 231645 and 231564 is 81 The difference of 231654 and 231645 is 9 The difference of 234156 and 231654 is 2502 The difference of 234165 and 234156 is 9 The difference of 234516 and 234165 is 351 The difference of 234561 and 234516 is 45 The difference of 234615 and 234561 is 54 The difference of 234651 and 234615 is 36 The difference of 235146 and 234651 is 495 The difference of 235164 and 235146 is 18 The difference of 235416 and 235164 is 252 The difference of 235461 and 235416 is 45 The difference of 235614 and 235461 is 153 The difference of 235641 and 235614 is 27 The difference of 236145 and 235641 is 504 The difference of 236154 and 236145 is 9 The difference of 236415 and 236154 is 261 The difference of 236451 and 236415 is 36 The difference of 236514 and 236451 is 63 The difference of 236541 and 236514 is 27 The difference of 241356 and 236541 is 4815 The difference of 241365 and 241356 is 9 The difference of 241536 and 241365 is 171 The difference of 241563 and 241536 is 27 The difference of 241635 and 241563 is 72 The difference of 241653 and 241635 is 18 The difference of 243156 and 241653 is 1503 The difference of 243165 and 243156 is 9 The difference of 243516 and 243165 is 351 The difference of 243561 and 243516 is 45 The difference of 243615 and 243561 is 54 The difference of 243651 and 243615 is 36 The difference of 245136 and 243651 is 1485 The difference of 245163 and 245136 is 27 The difference of 245316 and 245163 is 153 The difference of 245361 and 245316 is 45 The difference of 245613 and 245361 is 252 The difference of 245631 and 245613 is 18 The difference of 246135 and 245631 is 504 The difference of 246153 and 246135 is 18 The difference of 246315 and 246153 is 162 The difference of 246351 and 246315 is 36 The difference of 246513 and 246351 is 162 The difference of 246531 and 246513 is 18 The difference of 251346 and 246531 is 4815 The difference of 251364 and 251346 is 18 The difference of 251436 and 251364 is 72 The difference of 251463 and 251436 is 27 The difference of 251634 and 251463 is 171 The difference of 251643 and 251634 is 9 The difference of 253146 and 251643 is 1503 The difference of 253164 and 253146 is 18 The difference of 253416 and 253164 is 252 The difference of 253461 and 253416 is 45 The difference of 253614 and 253461 is 153 The difference of 253641 and 253614 is 27 The difference of 254136 and 253641 is 495 The difference of 254163 and 254136 is 27 The difference of 254316 and 254163 is 153 The difference of 254361 and 254316 is 45 The difference of 254613 and 254361 is 252 The difference of 254631 and 254613 is 18 The difference of 256134 and 254631 is 1503 The difference of 256143 and 256134 is 9 The difference of 256314 and 256143 is 171 The difference of 256341 and 256314 is 27 The difference of 256413 and 256341 is 72 The difference of 256431 and 256413 is 18 The difference of 261345 and 256431 is 4914 The difference of 261354 and 261345 is 9 The difference of 261435 and 261354 is 81 The difference of 261453 and 261435 is 18 The difference of 261534 and 261453 is 81 The difference of 261543 and 261534 is 9 The difference of 263145 and 261543 is 1602 The difference of 263154 and 263145 is 9 The difference of 263415 and 263154 is 261 The difference of 263451 and 263415 is 36 The difference of 263514 and 263451 is 63 The difference of 263541 and 263514 is 27 The difference of 264135 and 263541 is 594 The difference of 264153 and 264135 is 18 The difference of 264315 and 264153 is 162 The difference of 264351 and 264315 is 36 The difference of 264513 and 264351 is 162 The difference of 264531 and 264513 is 18 The difference of 265134 and 264531 is 603 The difference of 265143 and 265134 is 9 The difference of 265314 and 265143 is 171 The difference of 265341 and 265314 is 27 The difference of 265413 and 265341 is 72 The difference of 265431 and 265413 is 18 The difference of 312456 and 265431 is 47025 The difference of 312465 and 312456 is 9 The difference of 312546 and 312465 is 81 The difference of 312564 and 312546 is 18 The difference of 312645 and 312564 is 81 The difference of 312654 and 312645 is 9 The difference of 314256 and 312654 is 1602 The difference of 314265 and 314256 is 9 The difference of 314526 and 314265 is 261 The difference of 314562 and 314526 is 36 The difference of 314625 and 314562 is 63 The difference of 314652 and 314625 is 27 The difference of 315246 and 314652 is 594 The difference of 315264 and 315246 is 18 The difference of 315426 and 315264 is 162 The difference of 315462 and 315426 is 36 The difference of 315624 and 315462 is 162 The difference of 315642 and 315624 is 18 The difference of 316245 and 315642 is 603 The difference of 316254 and 316245 is 9 The difference of 316425 and 316254 is 171 The difference of 316452 and 316425 is 27 The difference of 316524 and 316452 is 72 The difference of 316542 and 316524 is 18 The difference of 321456 and 316542 is 4914 The difference of 321465 and 321456 is 9 The difference of 321546 and 321465 is 81 The difference of 321564 and 321546 is 18 The difference of 321645 and 321564 is 81 The difference of 321654 and 321645 is 9 The difference of 324156 and 321654 is 2502 The difference of 324165 and 324156 is 9 The difference of 324516 and 324165 is 351 The difference of 324561 and 324516 is 45 The difference of 324615 and 324561 is 54 The difference of 324651 and 324615 is 36 The difference of 325146 and 324651 is 495 The difference of 325164 and 325146 is 18 The difference of 325416 and 325164 is 252 The difference of 325461 and 325416 is 45 The difference of 325614 and 325461 is 153 The difference of 325641 and 325614 is 27 The difference of 326145 and 325641 is 504 The difference of 326154 and 326145 is 9 The difference of 326415 and 326154 is 261 The difference of 326451 and 326415 is 36 The difference of 326514 and 326451 is 63 The difference of 326541 and 326514 is 27 The difference of 341256 and 326541 is 14715 The difference of 341265 and 341256 is 9 The difference of 341526 and 341265 is 261 The difference of 341562 and 341526 is 36 The difference of 341625 and 341562 is 63 The difference of 341652 and 341625 is 27 The difference of 342156 and 341652 is 504 The difference of 342165 and 342156 is 9 The difference of 342516 and 342165 is 351 The difference of 342561 and 342516 is 45 The difference of 342615 and 342561 is 54 The difference of 342651 and 342615 is 36 The difference of 345126 and 342651 is 2475 The difference of 345162 and 345126 is 36 The difference of 345216 and 345162 is 54 The difference of 345261 and 345216 is 45 The difference of 345612 and 345261 is 351 The difference of 345621 and 345612 is 9 The difference of 346125 and 345621 is 504 The difference of 346152 and 346125 is 27 The difference of 346215 and 346152 is 63 The difference of 346251 and 346215 is 36 The difference of 346512 and 346251 is 261 The difference of 346521 and 346512 is 9 The difference of 351246 and 346521 is 4725 The difference of 351264 and 351246 is 18 The difference of 351426 and 351264 is 162 The difference of 351462 and 351426 is 36 The difference of 351624 and 351462 is 162 The difference of 351642 and 351624 is 18 The difference of 352146 and 351642 is 504 The difference of 352164 and 352146 is 18 The difference of 352416 and 352164 is 252 The difference of 352461 and 352416 is 45 The difference of 352614 and 352461 is 153 The difference of 352641 and 352614 is 27 The difference of 354126 and 352641 is 1485 The difference of 354162 and 354126 is 36 The difference of 354216 and 354162 is 54 The difference of 354261 and 354216 is 45 The difference of 354612 and 354261 is 351 The difference of 354621 and 354612 is 9 The difference of 356124 and 354621 is 1503 The difference of 356142 and 356124 is 18 The difference of 356214 and 356142 is 72 The difference of 356241 and 356214 is 27 The difference of 356412 and 356241 is 171 The difference of 356421 and 356412 is 9 The difference of 361245 and 356421 is 4824 The difference of 361254 and 361245 is 9 The difference of 361425 and 361254 is 171 The difference of 361452 and 361425 is 27 The difference of 361524 and 361452 is 72 The difference of 361542 and 361524 is 18 The difference of 362145 and 361542 is 603 The difference of 362154 and 362145 is 9 The difference of 362415 and 362154 is 261 The difference of 362451 and 362415 is 36 The difference of 362514 and 362451 is 63 The difference of 362541 and 362514 is 27 The difference of 364125 and 362541 is 1584 The difference of 364152 and 364125 is 27 The difference of 364215 and 364152 is 63 The difference of 364251 and 364215 is 36 The difference of 364512 and 364251 is 261 The difference of 364521 and 364512 is 9 The difference of 365124 and 364521 is 603 The difference of 365142 and 365124 is 18 The difference of 365214 and 365142 is 72 The difference of 365241 and 365214 is 27 The difference of 365412 and 365241 is 171 The difference of 365421 and 365412 is 9 The difference of 412356 and 365421 is 46935 The difference of 412365 and 412356 is 9 The difference of 412536 and 412365 is 171 The difference of 412563 and 412536 is 27 The difference of 412635 and 412563 is 72 The difference of 412653 and 412635 is 18 The difference of 413256 and 412653 is 603 The difference of 413265 and 413256 is 9 The difference of 413526 and 413265 is 261 The difference of 413562 and 413526 is 36 The difference of 413625 and 413562 is 63 The difference of 413652 and 413625 is 27 The difference of 415236 and 413652 is 1584 The difference of 415263 and 415236 is 27 The difference of 415326 and 415263 is 63 The difference of 415362 and 415326 is 36 The difference of 415623 and 415362 is 261 The difference of 415632 and 415623 is 9 The difference of 416235 and 415632 is 603 The difference of 416253 and 416235 is 18 The difference of 416325 and 416253 is 72 The difference of 416352 and 416325 is 27 The difference of 416523 and 416352 is 171 The difference of 416532 and 416523 is 9 The difference of 421356 and 416532 is 4824 The difference of 421365 and 421356 is 9 The difference of 421536 and 421365 is 171 The difference of 421563 and 421536 is 27 The difference of 421635 and 421563 is 72 The difference of 421653 and 421635 is 18 The difference of 423156 and 421653 is 1503 The difference of 423165 and 423156 is 9 The difference of 423516 and 423165 is 351 The difference of 423561 and 423516 is 45 The difference of 423615 and 423561 is 54 The difference of 423651 and 423615 is 36 The difference of 425136 and 423651 is 1485 The difference of 425163 and 425136 is 27 The difference of 425316 and 425163 is 153 The difference of 425361 and 425316 is 45 The difference of 425613 and 425361 is 252 The difference of 425631 and 425613 is 18 The difference of 426135 and 425631 is 504 The difference of 426153 and 426135 is 18 The difference of 426315 and 426153 is 162 The difference of 426351 and 426315 is 36 The difference of 426513 and 426351 is 162 The difference of 426531 and 426513 is 18 The difference of 431256 and 426531 is 4725 The difference of 431265 and 431256 is 9 The difference of 431526 and 431265 is 261 The difference of 431562 and 431526 is 36 The difference of 431625 and 431562 is 63 The difference of 431652 and 431625 is 27 The difference of 432156 and 431652 is 504 The difference of 432165 and 432156 is 9 The difference of 432516 and 432165 is 351 The difference of 432561 and 432516 is 45 The difference of 432615 and 432561 is 54 The difference of 432651 and 432615 is 36 The difference of 435126 and 432651 is 2475 The difference of 435162 and 435126 is 36 The difference of 435216 and 435162 is 54 The difference of 435261 and 435216 is 45 The difference of 435612 and 435261 is 351 The difference of 435621 and 435612 is 9 The difference of 436125 and 435621 is 504 The difference of 436152 and 436125 is 27 The difference of 436215 and 436152 is 63 The difference of 436251 and 436215 is 36 The difference of 436512 and 436251 is 261 The difference of 436521 and 436512 is 9 The difference of 451236 and 436521 is 14715 The difference of 451263 and 451236 is 27 The difference of 451326 and 451263 is 63 The difference of 451362 and 451326 is 36 The difference of 451623 and 451362 is 261 The difference of 451632 and 451623 is 9 The difference of 452136 and 451632 is 504 The difference of 452163 and 452136 is 27 The difference of 452316 and 452163 is 153 The difference of 452361 and 452316 is 45 The difference of 452613 and 452361 is 252 The difference of 452631 and 452613 is 18 The difference of 453126 and 452631 is 495 The difference of 453162 and 453126 is 36 The difference of 453216 and 453162 is 54 The difference of 453261 and 453216 is 45 The difference of 453612 and 453261 is 351 The difference of 453621 and 453612 is 9 The difference of 456123 and 453621 is 2502 The difference of 456132 and 456123 is 9 The difference of 456213 and 456132 is 81 The difference of 456231 and 456213 is 18 The difference of 456312 and 456231 is 81 The difference of 456321 and 456312 is 9 The difference of 461235 and 456321 is 4914 The difference of 461253 and 461235 is 18 The difference of 461325 and 461253 is 72 The difference of 461352 and 461325 is 27 The difference of 461523 and 461352 is 171 The difference of 461532 and 461523 is 9 The difference of 462135 and 461532 is 603 The difference of 462153 and 462135 is 18 The difference of 462315 and 462153 is 162 The difference of 462351 and 462315 is 36 The difference of 462513 and 462351 is 162 The difference of 462531 and 462513 is 18 The difference of 463125 and 462531 is 594 The difference of 463152 and 463125 is 27 The difference of 463215 and 463152 is 63 The difference of 463251 and 463215 is 36 The difference of 463512 and 463251 is 261 The difference of 463521 and 463512 is 9 The difference of 465123 and 463521 is 1602 The difference of 465132 and 465123 is 9 The difference of 465213 and 465132 is 81 The difference of 465231 and 465213 is 18 The difference of 465312 and 465231 is 81 The difference of 465321 and 465312 is 9 The difference of 512346 and 465321 is 47025 The difference of 512364 and 512346 is 18 The difference of 512436 and 512364 is 72 The difference of 512463 and 512436 is 27 The difference of 512634 and 512463 is 171 The difference of 512643 and 512634 is 9 The difference of 513246 and 512643 is 603 The difference of 513264 and 513246 is 18 The difference of 513426 and 513264 is 162 The difference of 513462 and 513426 is 36 The difference of 513624 and 513462 is 162 The difference of 513642 and 513624 is 18 The difference of 514236 and 513642 is 594 The difference of 514263 and 514236 is 27 The difference of 514326 and 514263 is 63 The difference of 514362 and 514326 is 36 The difference of 514623 and 514362 is 261 The difference of 514632 and 514623 is 9 The difference of 516234 and 514632 is 1602 The difference of 516243 and 516234 is 9 The difference of 516324 and 516243 is 81 The difference of 516342 and 516324 is 18 The difference of 516423 and 516342 is 81 The difference of 516432 and 516423 is 9 The difference of 521346 and 516432 is 4914 The difference of 521364 and 521346 is 18 The difference of 521436 and 521364 is 72 The difference of 521463 and 521436 is 27 The difference of 521634 and 521463 is 171 The difference of 521643 and 521634 is 9 The difference of 523146 and 521643 is 1503 The difference of 523164 and 523146 is 18 The difference of 523416 and 523164 is 252 The difference of 523461 and 523416 is 45 The difference of 523614 and 523461 is 153 The difference of 523641 and 523614 is 27 The difference of 524136 and 523641 is 495 The difference of 524163 and 524136 is 27 The difference of 524316 and 524163 is 153 The difference of 524361 and 524316 is 45 The difference of 524613 and 524361 is 252 The difference of 524631 and 524613 is 18 The difference of 526134 and 524631 is 1503 The difference of 526143 and 526134 is 9 The difference of 526314 and 526143 is 171 The difference of 526341 and 526314 is 27 The difference of 526413 and 526341 is 72 The difference of 526431 and 526413 is 18 The difference of 531246 and 526431 is 4815 The difference of 531264 and 531246 is 18 The difference of 531426 and 531264 is 162 The difference of 531462 and 531426 is 36 The difference of 531624 and 531462 is 162 The difference of 531642 and 531624 is 18 The difference of 532146 and 531642 is 504 The difference of 532164 and 532146 is 18 The difference of 532416 and 532164 is 252 The difference of 532461 and 532416 is 45 The difference of 532614 and 532461 is 153 The difference of 532641 and 532614 is 27 The difference of 534126 and 532641 is 1485 The difference of 534162 and 534126 is 36 The difference of 534216 and 534162 is 54 The difference of 534261 and 534216 is 45 The difference of 534612 and 534261 is 351 The difference of 534621 and 534612 is 9 The difference of 536124 and 534621 is 1503 The difference of 536142 and 536124 is 18 The difference of 536214 and 536142 is 72 The difference of 536241 and 536214 is 27 The difference of 536412 and 536241 is 171 The difference of 536421 and 536412 is 9 The difference of 541236 and 536421 is 4815 The difference of 541263 and 541236 is 27 The difference of 541326 and 541263 is 63 The difference of 541362 and 541326 is 36 The difference of 541623 and 541362 is 261 The difference of 541632 and 541623 is 9 The difference of 542136 and 541632 is 504 The difference of 542163 and 542136 is 27 The difference of 542316 and 542163 is 153 The difference of 542361 and 542316 is 45 The difference of 542613 and 542361 is 252 The difference of 542631 and 542613 is 18 The difference of 543126 and 542631 is 495 The difference of 543162 and 543126 is 36 The difference of 543216 and 543162 is 54 The difference of 543261 and 543216 is 45 The difference of 543612 and 543261 is 351 The difference of 543621 and 543612 is 9 The difference of 546123 and 543621 is 2502 The difference of 546132 and 546123 is 9 The difference of 546213 and 546132 is 81 The difference of 546231 and 546213 is 18 The difference of 546312 and 546231 is 81 The difference of 546321 and 546312 is 9 The difference of 561234 and 546321 is 14913 The difference of 561243 and 561234 is 9 The difference of 561324 and 561243 is 81 The difference of 561342 and 561324 is 18 The difference of 561423 and 561342 is 81 The difference of 561432 and 561423 is 9 The difference of 562134 and 561432 is 702 The difference of 562143 and 562134 is 9 The difference of 562314 and 562143 is 171 The difference of 562341 and 562314 is 27 The difference of 562413 and 562341 is 72 The difference of 562431 and 562413 is 18 The difference of 563124 and 562431 is 693 The difference of 563142 and 563124 is 18 The difference of 563214 and 563142 is 72 The difference of 563241 and 563214 is 27 The difference of 563412 and 563241 is 171 The difference of 563421 and 563412 is 9 The difference of 564123 and 563421 is 702 The difference of 564132 and 564123 is 9 The difference of 564213 and 564132 is 81 The difference of 564231 and 564213 is 18 The difference of 564312 and 564231 is 81 The difference of 564321 and 564312 is 9 The difference of 612345 and 564321 is 48024 The difference of 612354 and 612345 is 9 The difference of 612435 and 612354 is 81 The difference of 612453 and 612435 is 18 The difference of 612534 and 612453 is 81 The difference of 612543 and 612534 is 9 The difference of 613245 and 612543 is 702 The difference of 613254 and 613245 is 9 The difference of 613425 and 613254 is 171 The difference of 613452 and 613425 is 27 The difference of 613524 and 613452 is 72 The difference of 613542 and 613524 is 18 The difference of 614235 and 613542 is 693 The difference of 614253 and 614235 is 18 The difference of 614325 and 614253 is 72 The difference of 614352 and 614325 is 27 The difference of 614523 and 614352 is 171 The difference of 614532 and 614523 is 9 The difference of 615234 and 614532 is 702 The difference of 615243 and 615234 is 9 The difference of 615324 and 615243 is 81 The difference of 615342 and 615324 is 18 The difference of 615423 and 615342 is 81 The difference of 615432 and 615423 is 9 The difference of 621345 and 615432 is 5913 The difference of 621354 and 621345 is 9 The difference of 621435 and 621354 is 81 The difference of 621453 and 621435 is 18 The difference of 621534 and 621453 is 81 The difference of 621543 and 621534 is 9 The difference of 623145 and 621543 is 1602 The difference of 623154 and 623145 is 9 The difference of 623415 and 623154 is 261 The difference of 623451 and 623415 is 36 The difference of 623514 and 623451 is 63 The difference of 623541 and 623514 is 27 The difference of 624135 and 623541 is 594 The difference of 624153 and 624135 is 18 The difference of 624315 and 624153 is 162 The difference of 624351 and 624315 is 36 The difference of 624513 and 624351 is 162 The difference of 624531 and 624513 is 18 The difference of 625134 and 624531 is 603 The difference of 625143 and 625134 is 9 The difference of 625314 and 625143 is 171 The difference of 625341 and 625314 is 27 The difference of 625413 and 625341 is 72 The difference of 625431 and 625413 is 18 The difference of 631245 and 625431 is 5814 The difference of 631254 and 631245 is 9 The difference of 631425 and 631254 is 171 The difference of 631452 and 631425 is 27 The difference of 631524 and 631452 is 72 The difference of 631542 and 631524 is 18 The difference of 632145 and 631542 is 603 The difference of 632154 and 632145 is 9 The difference of 632415 and 632154 is 261 The difference of 632451 and 632415 is 36 The difference of 632514 and 632451 is 63 The difference of 632541 and 632514 is 27 The difference of 634125 and 632541 is 1584 The difference of 634152 and 634125 is 27 The difference of 634215 and 634152 is 63 The difference of 634251 and 634215 is 36 The difference of 634512 and 634251 is 261 The difference of 634521 and 634512 is 9 The difference of 635124 and 634521 is 603 The difference of 635142 and 635124 is 18 The difference of 635214 and 635142 is 72 The difference of 635241 and 635214 is 27 The difference of 635412 and 635241 is 171 The difference of 635421 and 635412 is 9 The difference of 641235 and 635421 is 5814 The difference of 641253 and 641235 is 18 The difference of 641325 and 641253 is 72 The difference of 641352 and 641325 is 27 The difference of 641523 and 641352 is 171 The difference of 641532 and 641523 is 9 The difference of 642135 and 641532 is 603 The difference of 642153 and 642135 is 18 The difference of 642315 and 642153 is 162 The difference of 642351 and 642315 is 36 The difference of 642513 and 642351 is 162 The difference of 642531 and 642513 is 18 The difference of 643125 and 642531 is 594 The difference of 643152 and 643125 is 27 The difference of 643215 and 643152 is 63 The difference of 643251 and 643215 is 36 The difference of 643512 and 643251 is 261 The difference of 643521 and 643512 is 9 The difference of 645123 and 643521 is 1602 The difference of 645132 and 645123 is 9 The difference of 645213 and 645132 is 81 The difference of 645231 and 645213 is 18 The difference of 645312 and 645231 is 81 The difference of 645321 and 645312 is 9 The difference of 651234 and 645321 is 5913 The difference of 651243 and 651234 is 9 The difference of 651324 and 651243 is 81 The difference of 651342 and 651324 is 18 The difference of 651423 and 651342 is 81 The difference of 651432 and 651423 is 9 The difference of 652134 and 651432 is 702 The difference of 652143 and 652134 is 9 The difference of 652314 and 652143 is 171 The difference of 652341 and 652314 is 27 The difference of 652413 and 652341 is 72 The difference of 652431 and 652413 is 18 The difference of 653124 and 652431 is 693 The difference of 653142 and 653124 is 18 The difference of 653214 and 653142 is 72 The difference of 653241 and 653214 is 27 The difference of 653412 and 653241 is 171 The difference of 653421 and 653412 is 9 The difference of 654123 and 653421 is 702 The difference of 654132 and 654123 is 9 The difference of 654213 and 654132 is 81 The difference of 654231 and 654213 is 18 The difference of 654312 and 654231 is 81 The difference of 654321 and 654312 is 9

The largest difference is 48024, 612345 - 564321 and 213456 - 165432.(398889 apart) 2600:6C50:17F:B6F8:8D80:1576:9B3E:8F74 (talk) 23:23, 27 May 2019 (UTC)