Pětimístná čísla

Dvě n ciferné celé číslo se považuje za ekvivalentní, pokud jedno je permutací druhého. Najděte počet 5ciferných celých čísel, takových že žádné dvě nejsou ekvivalentní. Pokud se číslice 5,7,9 mohou objevit nejvýše jednou, kolik neekvivalentních 5místných celých čísel existuje?

Správná odpověď:

x = 1371

Postup správného řešení:

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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x₁₃₇₁=99999

Našel jsi chybu či nepřesnost? Prosím nám ji pošli.

Tipy na související online kalkulačky

Naše kalkulačka pro výpočet procent Vám pomůže rychle vypočítat různé typické úlohy s procenty.
Viz také naši kalkulačku permutaci.
Chceš si dát spočítat kombinační číslo?

K vyřešení této úlohy jsou potřebné tyto znalosti z matematiky:

kombinatorika

aritmetika

porovnávání

základní operace a pojmy

čísla

přirozená čísla

Úroveň náročnosti úkolu

9. ročník

Pětimístná čísla

Správná odpověď:

Postup správného řešení:

K vyřešení této úlohy jsou potřebné tyto znalosti z matematiky:

Související a podobné příklady: