Dve n

Dve n ciferné celé číslo sa považuje za ekvivalentné, ak jedno je permutáciou druhého. Nájdite počet 5-ciferných celých čísel, takých že žiadne dve nie sú ekvivalentné. Ak sa číslice 5,7,9 môžu objaviť najviac raz, koľko neekvivalentných 5-ciferných celých čísel existuje?

Správna odpoveď:

x = 1371

Postup správneho riešenia:

x₁=10000	x₂=10001	x₃=10002	x₄=10003	x₅=10004	x₆=10005	x₇=10006	x₈=10007	x₉=10008	x₁₀=10009
x₁₁=10011	x₁₂=10012	x₁₃=10013	x₁₄=10014	x₁₅=10015	x₁₆=10016	x₁₇=10017	x₁₈=10018	x₁₉=10019	x₂₀=10022
x₂₁=10023	x₂₂=10024	x₂₃=10025	x₂₄=10026	x₂₅=10027	x₂₆=10028	x₂₇=10029	x₂₈=10033	x₂₉=10034	x₃₀=10035
x₃₁=10036	x₃₂=10037	x₃₃=10038	x₃₄=10039	x₃₅=10044	x₃₆=10045	x₃₇=10046	x₃₈=10047	x₃₉=10048	x₄₀=10049
x₄₁=10056	x₄₂=10057	x₄₃=10058	x₄₄=10059	x₄₅=10067	x₄₆=10068	x₄₇=10069	x₄₈=10078	x₄₉=10079	x₅₀=10088
x₅₁=10089	x₅₂=10099	x₅₃=10111	x₅₄=10112	x₅₅=10113	x₅₆=10114	x₅₇=10115	x₅₈=10116	x₅₉=10117	x₆₀=10118
x₆₁=10119	x₆₂=10122	x₆₃=10123	x₆₄=10124	x₆₅=10125	x₆₆=10126	x₆₇=10127	x₆₈=10128	x₆₉=10129	x₇₀=10133
x₇₁=10134	x₇₂=10135	x₇₃=10136	x₇₄=10137	x₇₅=10138	x₇₆=10139	x₇₇=10144	x₇₈=10145	x₇₉=10146	x₈₀=10147
x₈₁=10148	x₈₂=10149	x₈₃=10156	x₈₄=10157	x₈₅=10158	x₈₆=10159	x₈₇=10167	x₈₈=10168	x₈₉=10169	x₉₀=10178
x₉₁=10179	x₉₂=10188	x₉₃=10189	x₉₄=10199	x₉₅=10222	x₉₆=10223	x₉₇=10224	x₉₈=10225	x₉₉=10226	x₁₀₀=10227
x₁₀₁=10228	x₁₀₂=10229	x₁₀₃=10233	x₁₀₄=10234	x₁₀₅=10235	x₁₀₆=10236	x₁₀₇=10237	x₁₀₈=10238	x₁₀₉=10239	x₁₁₀=10244
x₁₁₁=10245	x₁₁₂=10246	x₁₁₃=10247	x₁₁₄=10248	x₁₁₅=10249	x₁₁₆=10256	x₁₁₇=10257	x₁₁₈=10258	x₁₁₉=10259	x₁₂₀=10267
x₁₂₁=10268	x₁₂₂=10269	x₁₂₃=10278	x₁₂₄=10279	x₁₂₅=10288	x₁₂₆=10289	x₁₂₇=10299	x₁₂₈=10333	x₁₂₉=10334	x₁₃₀=10335
x₁₃₁=10336	x₁₃₂=10337	x₁₃₃=10338	x₁₃₄=10339	x₁₃₅=10344	x₁₃₆=10345	x₁₃₇=10346	x₁₃₈=10347	x₁₃₉=10348	x₁₄₀=10349
x₁₄₁=10356	x₁₄₂=10357	x₁₄₃=10358	x₁₄₄=10359	x₁₄₅=10367	x₁₄₆=10368	x₁₄₇=10369	x₁₄₈=10378	x₁₄₉=10379	x₁₅₀=10388
x₁₅₁=10389	x₁₅₂=10399	x₁₅₃=10444	x₁₅₄=10445	x₁₅₅=10446	x₁₅₆=10447	x₁₅₇=10448	x₁₅₈=10449	x₁₅₉=10456	x₁₆₀=10457
x₁₆₁=10458	x₁₆₂=10459	x₁₆₃=10467	x₁₆₄=10468	x₁₆₅=10469	x₁₆₆=10478	x₁₆₇=10479	x₁₆₈=10488	x₁₆₉=10489	x₁₇₀=10499
x₁₇₁=10567	x₁₇₂=10568	x₁₇₃=10569	x₁₇₄=10578	x₁₇₅=10579	x₁₇₆=10588	x₁₇₇=10589	x₁₇₈=10599	x₁₇₉=10678	x₁₈₀=10679
x₁₈₁=10688	x₁₈₂=10689	x₁₈₃=10699	x₁₈₄=10788	x₁₈₅=10789	x₁₈₆=10799	x₁₈₇=10888	x₁₈₈=10889	x₁₈₉=10899	x₁₉₀=10999
x₁₉₁=11111	x₁₉₂=11112	x₁₉₃=11113	x₁₉₄=11114	x₁₉₅=11115	x₁₉₆=11116	x₁₉₇=11117	x₁₉₈=11118	x₁₉₉=11119	x₂₀₀=11122
x₂₀₁=11123	x₂₀₂=11124	x₂₀₃=11125	x₂₀₄=11126	x₂₀₅=11127	x₂₀₆=11128	x₂₀₇=11129	x₂₀₈=11133	x₂₀₉=11134	x₂₁₀=11135
x₂₁₁=11136	x₂₁₂=11137	x₂₁₃=11138	x₂₁₄=11139	x₂₁₅=11144	x₂₁₆=11145	x₂₁₇=11146	x₂₁₈=11147	x₂₁₉=11148	x₂₂₀=11149
x₂₂₁=11156	x₂₂₂=11157	x₂₂₃=11158	x₂₂₄=11159	x₂₂₅=11167	x₂₂₆=11168	x₂₂₇=11169	x₂₂₈=11178	x₂₂₉=11179	x₂₃₀=11188
x₂₃₁=11189	x₂₃₂=11199	x₂₃₃=11222	x₂₃₄=11223	x₂₃₅=11224	x₂₃₆=11225	x₂₃₇=11226	x₂₃₈=11227	x₂₃₉=11228	x₂₄₀=11229
x₂₄₁=11233	x₂₄₂=11234	x₂₄₃=11235	x₂₄₄=11236	x₂₄₅=11237	x₂₄₆=11238	x₂₄₇=11239	x₂₄₈=11244	x₂₄₉=11245	x₂₅₀=11246
x₂₅₁=11247	x₂₅₂=11248	x₂₅₃=11249	x₂₅₄=11256	x₂₅₅=11257	x₂₅₆=11258	x₂₅₇=11259	x₂₅₈=11267	x₂₅₉=11268	x₂₆₀=11269
x₂₆₁=11278	x₂₆₂=11279	x₂₆₃=11288	x₂₆₄=11289	x₂₆₅=11299	x₂₆₆=11333	x₂₆₇=11334	x₂₆₈=11335	x₂₆₉=11336	x₂₇₀=11337
x₂₇₁=11338	x₂₇₂=11339	x₂₇₃=11344	x₂₇₄=11345	x₂₇₅=11346	x₂₇₆=11347	x₂₇₇=11348	x₂₇₈=11349	x₂₇₉=11356	x₂₈₀=11357
x₂₈₁=11358	x₂₈₂=11359	x₂₈₃=11367	x₂₈₄=11368	x₂₈₅=11369	x₂₈₆=11378	x₂₈₇=11379	x₂₈₈=11388	x₂₈₉=11389	x₂₉₀=11399
x₂₉₁=11444	x₂₉₂=11445	x₂₉₃=11446	x₂₉₄=11447	x₂₉₅=11448	x₂₉₆=11449	x₂₉₇=11456	x₂₉₈=11457	x₂₉₉=11458	x₃₀₀=11459
x₃₀₁=11467	x₃₀₂=11468	x₃₀₃=11469	x₃₀₄=11478	x₃₀₅=11479	x₃₀₆=11488	x₃₀₇=11489	x₃₀₈=11499	x₃₀₉=11567	x₃₁₀=11568
x₃₁₁=11569	x₃₁₂=11578	x₃₁₃=11579	x₃₁₄=11588	x₃₁₅=11589	x₃₁₆=11599	x₃₁₇=11678	x₃₁₈=11679	x₃₁₉=11688	x₃₂₀=11689
x₃₂₁=11699	x₃₂₂=11788	x₃₂₃=11789	x₃₂₄=11799	x₃₂₅=11888	x₃₂₆=11889	x₃₂₇=11899	x₃₂₈=11999	x₃₂₉=12222	x₃₃₀=12223
x₃₃₁=12224	x₃₃₂=12225	x₃₃₃=12226	x₃₃₄=12227	x₃₃₅=12228	x₃₃₆=12229	x₃₃₇=12233	x₃₃₈=12234	x₃₃₉=12235	x₃₄₀=12236
x₃₄₁=12237	x₃₄₂=12238	x₃₄₃=12239	x₃₄₄=12244	x₃₄₅=12245	x₃₄₆=12246	x₃₄₇=12247	x₃₄₈=12248	x₃₄₉=12249	x₃₅₀=12256
x₃₅₁=12257	x₃₅₂=12258	x₃₅₃=12259	x₃₅₄=12267	x₃₅₅=12268	x₃₅₆=12269	x₃₅₇=12278	x₃₅₈=12279	x₃₅₉=12288	x₃₆₀=12289
x₃₆₁=12299	x₃₆₂=12333	x₃₆₃=12334	x₃₆₄=12335	x₃₆₅=12336	x₃₆₆=12337	x₃₆₇=12338	x₃₆₈=12339	x₃₆₉=12344	x₃₇₀=12345
x₃₇₁=12346	x₃₇₂=12347	x₃₇₃=12348	x₃₇₄=12349	x₃₇₅=12356	x₃₇₆=12357	x₃₇₇=12358	x₃₇₈=12359	x₃₇₉=12367	x₃₈₀=12368
x₃₈₁=12369	x₃₈₂=12378	x₃₈₃=12379	x₃₈₄=12388	x₃₈₅=12389	x₃₈₆=12399	x₃₈₇=12444	x₃₈₈=12445	x₃₈₉=12446	x₃₉₀=12447
x₃₉₁=12448	x₃₉₂=12449	x₃₉₃=12456	x₃₉₄=12457	x₃₉₅=12458	x₃₉₆=12459	x₃₉₇=12467	x₃₉₈=12468	x₃₉₉=12469	x₄₀₀=12478
x₄₀₁=12479	x₄₀₂=12488	x₄₀₃=12489	x₄₀₄=12499	x₄₀₅=12567	x₄₀₆=12568	x₄₀₇=12569	x₄₀₈=12578	x₄₀₉=12579	x₄₁₀=12588
x₄₁₁=12589	x₄₁₂=12599	x₄₁₃=12678	x₄₁₄=12679	x₄₁₅=12688	x₄₁₆=12689	x₄₁₇=12699	x₄₁₈=12788	x₄₁₉=12789	x₄₂₀=12799
x₄₂₁=12888	x₄₂₂=12889	x₄₂₃=12899	x₄₂₄=12999	x₄₂₅=13333	x₄₂₆=13334	x₄₂₇=13335	x₄₂₈=13336	x₄₂₉=13337	x₄₃₀=13338
x₄₃₁=13339	x₄₃₂=13344	x₄₃₃=13345	x₄₃₄=13346	x₄₃₅=13347	x₄₃₆=13348	x₄₃₇=13349	x₄₃₈=13356	x₄₃₉=13357	x₄₄₀=13358
x₄₄₁=13359	x₄₄₂=13367	x₄₄₃=13368	x₄₄₄=13369	x₄₄₅=13378	x₄₄₆=13379	x₄₄₇=13388	x₄₄₈=13389	x₄₄₉=13399	x₄₅₀=13444
x₄₅₁=13445	x₄₅₂=13446	x₄₅₃=13447	x₄₅₄=13448	x₄₅₅=13449	x₄₅₆=13456	x₄₅₇=13457	x₄₅₈=13458	x₄₅₉=13459	x₄₆₀=13467
x₄₆₁=13468	x₄₆₂=13469	x₄₆₃=13478	x₄₆₄=13479	x₄₆₅=13488	x₄₆₆=13489	x₄₆₇=13499	x₄₆₈=13567	x₄₆₉=13568	x₄₇₀=13569
x₄₇₁=13578	x₄₇₂=13579	x₄₇₃=13588	x₄₇₄=13589	x₄₇₅=13599	x₄₇₆=13678	x₄₇₇=13679	x₄₇₈=13688	x₄₇₉=13689	x₄₈₀=13699
x₄₈₁=13788	x₄₈₂=13789	x₄₈₃=13799	x₄₈₄=13888	x₄₈₅=13889	x₄₈₆=13899	x₄₈₇=13999	x₄₈₈=14444	x₄₈₉=14445	x₄₉₀=14446
x₄₉₁=14447	x₄₉₂=14448	x₄₉₃=14449	x₄₉₄=14456	x₄₉₅=14457	x₄₉₆=14458	x₄₉₇=14459	x₄₉₈=14467	x₄₉₉=14468	x₅₀₀=14469
x₅₀₁=14478	x₅₀₂=14479	x₅₀₃=14488	x₅₀₄=14489	x₅₀₅=14499	x₅₀₆=14567	x₅₀₇=14568	x₅₀₈=14569	x₅₀₉=14578	x₅₁₀=14579
x₅₁₁=14588	x₅₁₂=14589	x₅₁₃=14599	x₅₁₄=14678	x₅₁₅=14679	x₅₁₆=14688	x₅₁₇=14689	x₅₁₈=14699	x₅₁₉=14788	x₅₂₀=14789
x₅₂₁=14799	x₅₂₂=14888	x₅₂₃=14889	x₅₂₄=14899	x₅₂₅=14999	x₅₂₆=15678	x₅₂₇=15679	x₅₂₈=15688	x₅₂₉=15689	x₅₃₀=15699
x₅₃₁=15788	x₅₃₂=15789	x₅₃₃=15799	x₅₃₄=15888	x₅₃₅=15889	x₅₃₆=15899	x₅₃₇=15999	x₅₃₈=16788	x₅₃₉=16789	x₅₄₀=16799
x₅₄₁=16888	x₅₄₂=16889	x₅₄₃=16899	x₅₄₄=16999	x₅₄₅=17888	x₅₄₆=17889	x₅₄₇=17899	x₅₄₈=17999	x₅₄₉=18888	x₅₅₀=18889
x₅₅₁=18899	x₅₅₂=18999	x₅₅₃=19999	x₅₅₄=20000	x₅₅₅=20002	x₅₅₆=20003	x₅₅₇=20004	x₅₅₈=20005	x₅₅₉=20006	x₅₆₀=20007
x₅₆₁=20008	x₅₆₂=20009	x₅₆₃=20022	x₅₆₄=20023	x₅₆₅=20024	x₅₆₆=20025	x₅₆₇=20026	x₅₆₈=20027	x₅₆₉=20028	x₅₇₀=20029
x₅₇₁=20033	x₅₇₂=20034	x₅₇₃=20035	x₅₇₄=20036	x₅₇₅=20037	x₅₇₆=20038	x₅₇₇=20039	x₅₇₈=20044	x₅₇₉=20045	x₅₈₀=20046
x₅₈₁=20047	x₅₈₂=20048	x₅₈₃=20049	x₅₈₄=20056	x₅₈₅=20057	x₅₈₆=20058	x₅₈₇=20059	x₅₈₈=20067	x₅₈₉=20068	x₅₉₀=20069
x₅₉₁=20078	x₅₉₂=20079	x₅₉₃=20088	x₅₉₄=20089	x₅₉₅=20099	x₅₉₆=20222	x₅₉₇=20223	x₅₉₈=20224	x₅₉₉=20225	x₆₀₀=20226
x₆₀₁=20227	x₆₀₂=20228	x₆₀₃=20229	x₆₀₄=20233	x₆₀₅=20234	x₆₀₆=20235	x₆₀₇=20236	x₆₀₈=20237	x₆₀₉=20238	x₆₁₀=20239
x₆₁₁=20244	x₆₁₂=20245	x₆₁₃=20246	x₆₁₄=20247	x₆₁₅=20248	x₆₁₆=20249	x₆₁₇=20256	x₆₁₈=20257	x₆₁₉=20258	x₆₂₀=20259
x₆₂₁=20267	x₆₂₂=20268	x₆₂₃=20269	x₆₂₄=20278	x₆₂₅=20279	x₆₂₆=20288	x₆₂₇=20289	x₆₂₈=20299	x₆₂₉=20333	x₆₃₀=20334
x₆₃₁=20335	x₆₃₂=20336	x₆₃₃=20337	x₆₃₄=20338	x₆₃₅=20339	x₆₃₆=20344	x₆₃₇=20345	x₆₃₈=20346	x₆₃₉=20347	x₆₄₀=20348
x₆₄₁=20349	x₆₄₂=20356	x₆₄₃=20357	x₆₄₄=20358	x₆₄₅=20359	x₆₄₆=20367	x₆₄₇=20368	x₆₄₈=20369	x₆₄₉=20378	x₆₅₀=20379
x₆₅₁=20388	x₆₅₂=20389	x₆₅₃=20399	x₆₅₄=20444	x₆₅₅=20445	x₆₅₆=20446	x₆₅₇=20447	x₆₅₈=20448	x₆₅₉=20449	x₆₆₀=20456
x₆₆₁=20457	x₆₆₂=20458	x₆₆₃=20459	x₆₆₄=20467	x₆₆₅=20468	x₆₆₆=20469	x₆₆₇=20478	x₆₆₈=20479	x₆₆₉=20488	x₆₇₀=20489
x₆₇₁=20499	x₆₇₂=20567	x₆₇₃=20568	x₆₇₄=20569	x₆₇₅=20578	x₆₇₆=20579	x₆₇₇=20588	x₆₇₈=20589	x₆₇₉=20599	x₆₈₀=20678
x₆₈₁=20679	x₆₈₂=20688	x₆₈₃=20689	x₆₈₄=20699	x₆₈₅=20788	x₆₈₆=20789	x₆₈₇=20799	x₆₈₈=20888	x₆₈₉=20889	x₆₉₀=20899
x₆₉₁=20999	x₆₉₂=22222	x₆₉₃=22223	x₆₉₄=22224	x₆₉₅=22225	x₆₉₆=22226	x₆₉₇=22227	x₆₉₈=22228	x₆₉₉=22229	x₇₀₀=22233
x₇₀₁=22234	x₇₀₂=22235	x₇₀₃=22236	x₇₀₄=22237	x₇₀₅=22238	x₇₀₆=22239	x₇₀₇=22244	x₇₀₈=22245	x₇₀₉=22246	x₇₁₀=22247
x₇₁₁=22248	x₇₁₂=22249	x₇₁₃=22256	x₇₁₄=22257	x₇₁₅=22258	x₇₁₆=22259	x₇₁₇=22267	x₇₁₈=22268	x₇₁₉=22269	x₇₂₀=22278
x₇₂₁=22279	x₇₂₂=22288	x₇₂₃=22289	x₇₂₄=22299	x₇₂₅=22333	x₇₂₆=22334	x₇₂₇=22335	x₇₂₈=22336	x₇₂₉=22337	x₇₃₀=22338
x₇₃₁=22339	x₇₃₂=22344	x₇₃₃=22345	x₇₃₄=22346	x₇₃₅=22347	x₇₃₆=22348	x₇₃₇=22349	x₇₃₈=22356	x₇₃₉=22357	x₇₄₀=22358
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x₁₃₄₁=70089	x₁₃₄₂=70099	x₁₃₄₃=70888	x₁₃₄₄=70889	x₁₃₄₅=70899	x₁₃₄₆=70999	x₁₃₄₇=78888	x₁₃₄₈=78889	x₁₃₄₉=78899	x₁₃₅₀=78999
x₁₃₅₁=79999	x₁₃₅₂=80000	x₁₃₅₃=80008	x₁₃₅₄=80009	x₁₃₅₅=80088	x₁₃₅₆=80089	x₁₃₅₇=80099	x₁₃₅₈=80888	x₁₃₅₉=80889	x₁₃₆₀=80899
x₁₃₆₁=80999	x₁₃₆₂=88888	x₁₃₆₃=88889	x₁₃₆₄=88899	x₁₃₆₅=88999	x₁₃₆₆=89999	x₁₃₆₇=90000	x₁₃₆₈=90009	x₁₃₆₉=90099	x₁₃₇₀=90999
x₁₃₇₁=99999

Našiel si chybu či nepresnosť? Kľudne nám ju napíš.

Tipy na súvisiace online kalkulačky

Naša kalkulačka na výpočet percent Vám pomôže rýchlo vypočítať rôzne typické úlohy s percentami.
Pozrite aj našu kalkulačku permutácií.
Chceš si dať zrátať kombinačné číslo?

Na vyriešenie tejto úlohy sú potrebné tieto znalosti z matematiky:

kombinatorika

aritmetika

porovnávanie

základné operácie a pojmy

čísla

prirodzené čísla

Úroveň náročnosti úlohy

9. ročník

Odporúčame k tejto úlohe z matematiky si pozrieť toto výukové video: video1 video2 video3 video4

Dve n

Správna odpoveď:

Postup správneho riešenia:

Na vyriešenie tejto úlohy sú potrebné tieto znalosti z matematiky:

Súvisiace a podobné príklady: