|
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
Nombres complémentés à 999… ou à 1000… Quels
sont les nombres qui ont le même jeu de chiffres que leur différence avec 999
ou avec 1000 ? Ex: 1000 – 185 = 815:
chiffres 1, 8 et 5 999 – 118 = 881: chiffres 1 et 8 |
|
|
|||
|
1 chiffre |
0 |
/ |
|
|
2 chiffres |
8 |
18, 27, 36, 45, 54, 63, 72, 81 Exemple: 99 – 18 = 81
& 99 – 81 = 18 Observez que la liste est bien symétrique. |
|
|
3 |
24 |
118,
181, 188, 227, 272, 277, 336, 363, 366, 445, 454, 455, 544, 545, 554, 633,
636, 663, 722, 727, 772, 811, 818, 881 Deux
chiffres identiques de 1 à 8 et le troisième est le complément à 9 de
ceux-ci. Ils sont huit de base: 118, 227, 336, 445, 554, 663, 772, 881. Chacun
avec trois possibilités, comme 118, 181 et 188. |
|
|
4 |
248 |
1089, 1098,
1118, 1181, 1188, 1278, 1287, 1368, 1386, 1458, 1485, 1548, 1584, 1638, 1683,
1728, 1782, 1809, 1811, 1818, 1827, 1836, 1845, 1854, 1863, 1872, 1881, 1888,
1890, 1908, 1980, 2079, 2097, 2178, 2187,
2227, 2272, 2277, 2367, 2376, 2457, 2475, 2547, 2574, 2637, 2673, 2709, 2718,
2722, 2727, 2736, 2745, 2754, 2763, 2772, 2777, 2781, 2790, 2817, 2871, 2907,
2970, 3069, 3096, 3168, 3186, 3267, 3276, 3336, 3363, 3366, 3456, 3465, 3546,
3564, 3609, 3618, 3627, 3633, 3636, 3645, 3654, 3663, 3666, 3672, 3681, 3690,
3726, 3762, 3816, 3861, 3906, 3960, 4059, 4095, 4158, 4185, 4257, 4275, 4356,
4365, 4445, 4454, 4455, 4509, 4518, 4527, 4536, 4544, 4545, 4554, 4555, 4563,
4572, 4581, 4590, 4635, 4653, 4725, 4752, 4815, 4851, 4905, 4950, 5049, 5094,
5148, 5184, 5247, 5274, 5346, 5364, 5409, 5418, 5427, 5436, 5444, 5445, 5454,
5455, 5463, 5472, 5481, 5490, 5544, 5545, 5554, 5634, 5643, 5724, 5742, 5814,
5841, 5904, 5940, 6039, 6093, 6138, 6183, 6237, 6273, 6309, 6318, 6327, 6333,
6336, 6345, 6354, 6363, 6366, 6372, 6381, 6390, 6435, 6453, 6534, 6543, 6633,
6636, 6663, 6723, 6732, 6813, 6831, 6903, 6930, 7029, 7092, 7128, 7182, 7209,
7218, 7222, 7227, 7236, 7245, 7254, 7263, 7272, 7277, 7281, 7290, 7326, 7362,
7425, 7452, 7524, 7542, 7623, 7632, 7722, 7727, 7772, 7812, 7821, 7902, 7920,
8019, 8091, 8109, 8111, 8118, 8127, 8136, 8145, 8154, 8163, 8172, 8181, 8188,
8190, 8217, 8271, 8316, 8361, 8415, 8451, 8514, 8541, 8613, 8631, 8712, 8721,
8811, 8818, 8881, 8901, 8910 |
|
|
5 |
2 040 |
10089, 10098, 10189, 10198, 10809, 10819,
10889, 10890, 10891, 10898, 10899, 10908, 10918, 10980, 10981, 10988, 10989, 10998,
11089, 11098, 11118, 11181, 11188, 11278, 11287, 11368, 11386, 11458, 11485,
11548, 11584, 11638, 11683, 11728, 11782, 11809, 11811, 11818, 11827, 11836,
11845, 11854, 11863, 11872, 11881, 11888, 11890, 11908, 11980, 12178, 12187,
12278, 12287, 12718, 12728, 12778, 12781, 12782, 12787, 12788, 12817, 12827,
12871, 12872, 12877, 12878, 12887, 13168, 13186, 13368, 13386, 13618, 13638,
13668, 13681, 13683, 13686, 13688, 13816, 13836, 13861, 13863, 13866, 13868,
13886, 14158, 14185, 14458, 14485, 14518, 14548, 14558, 14581, 14584, 14585,
14588, 14815, 14845, 14851, 14854, 14855, 14858, 14885, 15148, 15184, 15418,
15448, 15458, 15481, 15484, 15485, 15488, 15548, 15584, 15814, 15841, 15844,
15845, 15848, 15854, 15884, 16138, 16183, 16318, 16338, 16368, 16381, 16383,
16386, 16388, 16638, 16683, 16813, 16831, 16833, 16836, 16838, 16863, 16883,
17128, 17182, 17218, 17228, 17278, 17281, 17282, 17287, 17288, 17728, 17782,
17812, 17821, 17822, 17827, 17828, 17872, 17882, 18009, 18019, 18089, 18090,
18091, 18098, 18099, 18109, 18111, 18118, 18127, 18136, 18145, 18154, 18163,
18172, 18181, 18188, 18190, 18217, 18227, 18271, 18272, 18277, 18278, 18287,
18316, 18336, 18361, 18363, 18366, 18368, 18386, 18415, 18445, 18451, 18454,
18455, 18458, 18485, 18514, 18541, 18544, 18545, 18548, 18554, 18584, 18613,
18631, 18633, 18636, 18638, 18663, 18683, 18712, 18721, 18722, 18727, 18728,
18772, 18782, 18809, 18811, 18818, 18827, 18836, 18845, 18854, 18863, 18872,
18881, 18888, 18890, 18900, 18901, 18908, 18909, 18910, 18980, 18990, 19008,
19018, 19080, 19081, 19088, 19089, 19098, 19108, 19180, 19800, 19801, 19808,
19809, 19810, 19880, 19890, 19908, 19980, 20079, …. 88118, 88127, 88136, 88145, 88154, 88163,
88172, 88181, 88188, 88190, 88217, 88271, 88316, 88361, 88415, 88451, 88514,
88541, 88613, 88631, 88712, 88721, 88811, 88818, 88881, 88901, 88910, 89001,
89010, 89011, 89018, 89019, 89081, 89091, 89100, 89101, 89108, 89109, 89110,
89180, 89190, 89801, 89810, 89901, 89910 |
|
|
6 |
18
488 |
100089 … 899910 |
|
|
|
|||
|
1 chiffre |
1 |
5 |
|
|
2 |
1 |
50 |
|
|
3 |
9 |
185, 275,
365, 455, 500, 545, 635, 725, 815 Exemple: 1000 – 185 = 815
& 1000 – 815 = 185 Observez que la liste est bien symétrique. |
|
|
4 |
33 |
1185,
1815, 1850, 1885, 2275, 2725, 2750, 2775, 3365, 3635, 3650, 3665, 4455, 4545,
4550, 4555, 5000, 5445, 5450, 5455, 5545, 6335, 6350, 6365, 6635, 7225, 7250,
7275, 7725, 8115, 8150, 8185, 8815 |
|
|
5 |
457 |
10890, 10891, 10895, 10899, 10981, 10985,
10989, 11185, 11815, 11850, 11885, 12782, 12785, 12788, 12872, 12875, 12878,
13685, 13865, 14585, 14855, 15485, 15845, 16385, 16835, 17282, 17285, 17288,
17822, 17825, 17828, 18090, 18091, 18095, 18099, 18115, 18150, 18185, 18272,
18275, 18278, 18365, 18455, 18500, 18545, 18635, 18722, 18725, 18728, 18815,
18850, 18885, 18901, 18905, 18909, 18910, 19081, 19085, 19089, 19801, 19805,
19809, 19810, 20795, … 79205, 80190, 80191, 80195, 80199, 80911,
80915, 80919, 81090, 81091, 81095, 81099, 81115, 81150, 81185, 81272, 81275,
81278, 81365, 81455, 81500, 81545, 81635, 81722, 81725, 81728, 81815, 81850,
81885, 81901, 81905, 81909, 81910, 82172, 82175, 82178, 82712, 82715, 82718,
83165, 83615, 84155, 84515, 85145, 85415, 86135, 86315, 87122, 87125, 87128,
87212, 87215, 87218, 88115, 88150, 88185, 88815, 89011, 89015, 89019, 89101,
89105, 89109, 89110 |
|
|
6 |
4 225 |
100890 … 899110 |
|
|
Nombres complémentés à 999… |
|
||
|
1 chiffre |
0 |
/ |
|
|
2 |
0 |
Exemple: 99 – 18 = 81
& 99 – 81 = 18 Observez que la liste est bien symétrique. |
|
|
3 |
8 |
209,
308, 407, 506, 605, 704, 803, 902 Exemple: 1111 – 209 = 902
& 1111 – 902 = 209 Observez que la liste est bien symétrique. |
|
|
4 |
28 |
2059, 3058, 4057, 4565, 4566, 4655, 4656, 5056,
5209, 5308, 5407, 5465, 5466, 5506, 5605, 5645, 5646, 5704, 5803, 5902, 6055,
6455, 6456, 6545, 6546, 7054, 8053, 9052 |
|
|
5 |
520 |
12009, 12090, 12099, 12892, 12899, 12982,
12989, 13098, 14097, 15096, 16095, 17094, 18093, 18292, 18299, 18922, 18929,
19002, 19020, 19092, 19209, 19282, 19289, 19308, 19407, 19506, 19605, 19704,
19803, 19822, 19829, 19902, 20019, … 97014, 98013, 98122, 98129, 98212, 98219,
99012, 99021, 99102 |
|
|
6 |
5 540 |
112009 … 999102 |
|
