Hány olyan pozitív egész szám van, amiben a számjegyek reciprokának összege 1?

1, 22, 333, 4444, ...

244, 2488, ...

Így kell érteni, hogy a számjegyek reciprokainak összege 1?

Mert akkor végtelen.

#2 Jaj, tényleg, de hülye vagyok! :)

#3 0-nak nincs reciproka. Mivel szorzod meg, hogy 1 legyen?

Amúgy véletlenül nem csak a háromjegyűek száma kell?

Elég sok van... Ötjegyűig itt egy lista:

1

22

236, 244, 263, 326, 333, 362, 424, 442, 623, 632

2488, 2666, 2848, 2884, 3366, 3446, 3464, 3636, 3644, 3663, 4288, 4346, 4364, 4436, 4444, 4463, 4634, 4643, 4828, 4882, 6266, 6336, 6344, 6363, 6434, 6443, 6626, 6633, 6662, 8248, 8284, 8428, 8482, 8824, 8842

26999, 28888, 29699, 29969, 29996, 33999, 34688, 34868, 34886, 36488, 36666, 36848, 36884, 38468, 38486, 38648, 38684, 38846, 38864, 39399, 39939, 39993, 43688, 43868, 43886, 44488, 44666, 44848, 44884, 46388, 46466, 46646, 46664, 46838, 46883, 48368, 48386, 48448, 48484, 48638, 48683, 48836, 48844, 48863, 55555, 62999, 63488, 63666, 63848, 63884, 64388, 64466, 64646, 64664, 64838, 64883, 66366, 66446, 66464, 66636, 66644, 66663, 68348, 68384, 68438, 68483, 68834, 68843, 69299, 69929, 69992, 82888, 83468, 83486, 83648, 83684, 83846, 83864, 84368, 84386, 84448, 84484, 84638, 84683, 84836, 84844, 84863, 86348, 86384, 86438, 86483, 86834, 86843, 88288, 88346, 88364, 88436, 88444, 88463, 88634, 88643, 88828, 88882, 92699, 92969, 92996, 93399, 93939, 93993, 96299, 96929, 96992, 99269, 99296, 99339, 99393, 99629, 99692, 99926, 99933, 99962

366999, 368888, 369699, 369969, 369996, 386888, 388688, 388868, 388886, 396699, 396969, 396996, 399669, 399696, 399966, 446999, 448888, 449699, 449969, 449996, 464999, 466688, 466868, 466886, 468668, 468686, 468866, 469499, 469949, 469994, 484888, 486668, 486686, 486866, 488488, 488666, 488848, 488884, 494699, 494969, 494996, 496499, 496949, 496994, 499469, 499496, 499649, 499694, 499946, 499964, 636999, 638888, 639699, 639969, 639996, 644999, 646688, 646868, 646886, 648668, 648686, 648866, 649499, 649949, 649994, 663999, 664688, 664868, 664886, 666488, 666666, 666848, 666884, 668468, 668486, 668648, 668684, 668846, 668864, 669399, 669939, 669993, 683888, 684668, 684686, 684866, 686468, 686486, 686648, 686684, 686846, 686864, 688388, 688466, 688646, 688664, 688838, 688883, 693699, 693969, 693996, 694499, 694949, 694994, 696399, 696939, 696993, 699369, 699396, 699449, 699494, 699639, 699693, 699936, 699944, 699963, 836888, 838688, 838868, 838886, 844888, 846668, 846686, 846866, 848488, 848666, 848848, 848884, 863888, 864668, 864686, 864866, 866468, 866486, 866648, 866684, 866846, 866864, 868388, 868466, 868646, 868664, 868838, 868883, 883688, 883868, 883886, 884488, 884666, 884848, 884884, 886388, 886466, 886646, 886664, 886838, 886883, 888368, 888386, 888448, 888484, 888638, 888683, 888836, 888844, 888863, 936699, 936969, 936996, 939669, 939696, 939966, 944699, 944969, 944996, 946499, 946949, 946994, 949469, 949496, 949649, 949694, 949946, 949964, 963699, 963969, 963996, 964499, 964949, 964994, 966399, 966939, 966993, 969369, 969396, 969449, 969494, 969639, 969693, 969936, 969944, 969963, 993669, 993696, 993966, 994469, 994496, 994649, 994694, 994946, 994964, 996369, 996396, 996449, 996494, 996639, 996693, 996936, 996944, 996963, 999366, 999446, 999464, 999636, 999644, 999663