Each of the positive integers is pandigital such that

>>

>> is also pandigital

>>

>>

Find

Here's one solution:

Each of the integers is pandigital

Find other solutions.

Paul found:

where is ten times a pandigital number:

And where is a pandigital number:

Format

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Here are all of them ( can’t guarantee that though 🙂 ).

Format is {a, b, c, d}.

{1076539482,2153078964,2691348705,4306157928}

{1098765432,2197530864,2746913580,4395061728}

{1234567890,2469135780,3086419725,4938271560}

{1234568790,2469137580,3086421975,4938275160}

{1269835704,2539671408,3174589260,5079342816}

{1270356984,2540713968,3175892460,5081427936}

{1274590368,2549180736,3186475920,5098361472}

{1298435670,2596871340,3246089175,5193742680}

{1365079482,2730158964,3412698705,5460317928}

{1367590482,2735180964,3418976205,5470361928}

{1472590368,2945180736,3681475920,5890361472}

{1476859032,2953718064,3692147580,5907436128}

{1479365082,2958730164,3698412705,5917460328}

{1564329870,3128659740,3910824675,6257319480}

{1587296430,3174592860,3968241075,6349185720}

{1274590368,3186475920,3186475920,5098361472}

{1507936482,3015872964,3769841205,6031745928}

{1526437098,3052874196,3816092745,6105748392}

{1642958730,3285917460,4107396825,6571834920}

{1705483926,3410967852,4263709815,6821935704}

{1728439506,3456879012,4321098765,6913758024}

{1759048632,3518097264,4397621580,7036194528}

{1472590368,3681475920,3681475920,5890361472}

{1847356290,3694712580,4618390725,7389425160}

{1950637284,3901274568,4876593210,7802549136}

{1962530874,3925061748,4906327185,7850123496}

{1962730854,3925461708,4906827135,7850923416}

{1962850734,3925701468,4907126835,7851402936}

{1975308642,3950617284,4938271605,7901234568}

{2107653948,4215307896,5269134870,8430615792}

{2136507948,4273015896,5341269870,8546031792}

{2136759048,4273518096,5341897620,8547036192}

{2147936508,4295873016,5369841270,8591746032}

{2150793648,4301587296,5376984120,8603174592}

{2197530864,4395061728,5493827160,8790123456}

{2409513678,4819027356,6023784195,9638054712}

Paul.

I had 29 solutions in mind, such that A + D is also pandigital.

You found 36. The seven extra solutions are also interesting since each of them is

10 times a pandigital number.

Your last seven solutions being:

{2107653948,4215307896,5269134870,8430615792}

2107653948+8430615792 = 10538269740

{2136507948,4273015896,5341269870,8546031792}

2136507948+8546031792 = 10682539740

{2136759048,4273518096,5341897620,8547036192}

2136759048+8547036192 = 10683795240

{2147936508,4295873016,5369841270,8591746032}

2147936508+8591746032 = 10739682540

{2150793648,4301587296,5376984120,8603174592}

2150793648+8603174592 = 10753968240

{2197530864,4395061728,5493827160,8790123456}

2197530864+8790123456 = 10987654320

{2409513678,4819027356,6023784195,9638054712}

2409513678+9638054712 = 12047568390

Here are a few more that aren’t with a<b<c<d.

A + D = B and the arithmetic mean of A & D is = C

1098765432 5493827160 2746913580 4395061728

1269835704 6349178520 3174589260 5079342816

1270356984 6351784920 3175892460 5081427936

1274590368 6372951840 3186475920 5098361472

1472590368 7362951840 3681475920 5890361472

1476859032 7384295160 3692147580 5907436128

1098765432 7691358024 2746913580 4395061728

1098765432 8790123456 2746913580 4395061728

1759048632 8795243160 4397621580 7036194528

1950637284 9753186420 4876593210 7802549136

1234567890 9876543120 3086419725 4938271560

the geometric mean od A & D is

2197530864

2539671408

2540713968

2549180736

2945180736

2953718064

2197530864

2197530864

3518097264

3901274568

2469135780

Paul.

Thanks for the additional research