Z9-I-4

Katka si myslela pětimístné přirozené číslo. Do sešitu napsala na první řádek součet myšleného čísla a poloviny myšleného čísla. Na druhý řádek napsala součet myšleného čísla a pětiny myšleného čísla. Na třetí řádek napsala součet myšleného čísla a devítiny myšleného čísla. Nakonec sečetla všechna tři zapsaná čísla a výsledek napsala na čtvrtý řádek. Poté s úžasem zjistila, že na čtvrtém řádku má zapsánu třetí mocninu jistého přirozeného čísla.

Určete nejmenší číslo, které si Katka mohla myslet na začátku.

Výsledek

n =  11250

Řešení:

Textové řešení n =







Napište nám komentář ke příkladu a řešení (například pokud je stále něco nejasné ...):

13 komentářů (18 odpovědí celkově):
#1
Žák
Jak jste došli k prvnímu číslu n=11250? Děkuji :)

2 roky  2 Likes
#2
Www
staci jet od cisla 10000 co je prvni 5-ti mistne cislo a testovat ho ci splna "vlastnosti"....

druha moznost je vypocitet treti odmocninu z 10000 = 21.544346 cize zacat od 223 , 233 az po 353 (co je jen 13 vyskusani vysledku)

#3
Žák
A nešlo by nějak matematicky vypočítat n? A ne ho pouze na začátku odhadnout?

2 roky  1 Like
#4
Žák
myslim ze neuplne reseni podpori Vasi kreativitu a na neco taky prijidete sami a budete se tesit... Ulohy MO nejsu ze stahnu z internetu a vsichni do tydne odovzdaji stejne reseni....

Hodne pile!

2 roky  2 Likes
#1
sewa :::) mas rozhodne pravdu :) a ale tak no ,,, kazdy svoje pochody a my ich nezmenime :)

2 roky  1 Like
#5
Týna
Kde jsi přišel na 35 na třetí? Jako, kde jsi to vzal? A proč si myslíš, že to bude zrovna tohle číslo? Děkuji za odpověď.

#6
Žák
Zde je počítačem vygenerované řešení
10000 = 33.6525, 10001 = 33.6533, 10002 = 33.6545, 10003 = 33.6557, 10004 = 33.6569, 10005 = 33.6581, 10006 = 33.6589, 10007 = 33.6601, 10008 = 33.6613, 10009 = 33.6625, 10010 = 33.6636, 10011 = 33.6648, 10012 = 33.6657, 10013 = 33.6669, 10014 = 33.668, 10015 = 33.6692, 10016 = 33.6704, 10017 = 33.6713, 10018 = 33.6725, 10019 = 33.6736, 10020 = 33.6748, 10021 = 33.676, 10022 = 33.6769, 10023 = 33.678, 10024 = 33.6792, 10025 = 33.6804, 10026 = 33.6816, 10027 = 33.6827, 10028 = 33.6836, 10029 = 33.6848, 10030 = 33.686, 10031 = 33.6872, 10032 = 33.6883, 10033 = 33.6892, 10034 = 33.6904, 10035 = 33.6916, 10036 = 33.6927, 10037 = 33.6939, 10038 = 33.6948, 10039 = 33.696, 10040 = 33.6971, 10041 = 33.6983, 10042 = 33.6995, 10043 = 33.7004, 10044 = 33.7015, 10045 = 33.7027, 10046 = 33.7039, 10047 = 33.7051, 10048 = 33.7062, 10049 = 33.7071, 10050 = 33.7083, 10051 = 33.7095, 10052 = 33.7106, 10053 = 33.7118, 10054 = 33.7127, 10055 = 33.7139, 10056 = 33.715, 10057 = 33.7162, 10058 = 33.7174, 10059 = 33.7183, 10060 = 33.7194, 10061 = 33.7206, 10062 = 33.7218, 10063 = 33.7229, 10064 = 33.7241, 10065 = 33.725, 10066 = 33.7262, 10067 = 33.7273, 10068 = 33.7285, 10069 = 33.7297, 10070 = 33.7306, 10071 = 33.7317, 10072 = 33.7329, 10073 = 33.7341, 10074 = 33.7353, 10075 = 33.7361, 10076 = 33.7373, 10077 = 33.7385, 10078 = 33.7397, 10079 = 33.7408, 10080 = 33.742, 10081 = 33.7429, 10082 = 33.744, 10083 = 33.7452, 10084 = 33.7464, 10085 = 33.7476, 10086 = 33.7484, 10087 = 33.7496, 10088 = 33.7508, 10089 = 33.7519, 10090 = 33.7531, 10091 = 33.754, 10092 = 33.7552, 10093 = 33.7563, 10094 = 33.7575, 10095 = 33.7587, 10096 = 33.7595, 10097 = 33.7607, 10098 = 33.7619, 10099 = 33.7631, 10100 = 33.7642, 10101 = 33.7654, 10102 = 33.7663, 10103 = 33.7674, 10104 = 33.7686, 10105 = 33.7698, 10106 = 33.771, 10107 = 33.7718, 10108 = 33.773, 10109 = 33.7742, 10110 = 33.7753, 10111 = 33.7765, 10112 = 33.7774, 10113 = 33.7785, 10114 = 33.7797, 10115 = 33.7809, 10116 = 33.7821, 10117 = 33.7832, 10118 = 33.7841, 10119 = 33.7853, 10120 = 33.7864, 10121 = 33.7876, 10122 = 33.7888, 10123 = 33.7896, 10124 = 33.7908, 10125 = 33.792, 10126 = 33.7932, 10127 = 33.7943, 10128 = 33.7952, 10129 = 33.7964, 10130 = 33.7975, 10131 = 33.7987, 10132 = 33.7999, 10133 = 33.8007, 10134 = 33.8019, 10135 = 33.8031, 10136 = 33.8042, 10137 = 33.8054, 10138 = 33.8066, 10139 = 33.8074, 10140 = 33.8086, 10141 = 33.8098, 10142 = 33.8109, 10143 = 33.8121, 10144 = 33.813, 10145 = 33.8142, 10146 = 33.8153, 10147 = 33.8165, 10148 = 33.8176, 10149 = 33.8185, 10150 = 33.8197, 10151 = 33.8209, 10152 = 33.822, 10153 = 33.8232, 10154 = 33.8244, 10155 = 33.8252, 10156 = 33.8264, 10157 = 33.8276, 10158 = 33.8287, 10159 = 33.8299, 10160 = 33.8308, 10161 = 33.8319, 10162 = 33.8331, 10163 = 33.8343, 10164 = 33.8354, 10165 = 33.8363, 10166 = 33.8375, 10167 = 33.8386, 10168 = 33.8398, 10169 = 33.841, 10170 = 33.8421, 10171 = 33.843, 10172 = 33.8442, 10173 = 33.8453, 10174 = 33.8465, 10175 = 33.8476, 10176 = 33.8485, 10177 = 33.8497, 10178 = 33.8508, 10179 = 33.852, 10180 = 33.8532, 10181 = 33.854, 10182 = 33.8552, 10183 = 33.8564, 10184 = 33.8575, 10185 = 33.8587, 10186 = 33.8596, 10187 = 33.8607, 10188 = 33.8619, 10189 = 33.8631, 10190 = 33.8642, 10191 = 33.8654, 10192 = 33.8663, 10193 = 33.8674, 10194 = 33.8686, 10195 = 33.8697, 10196 = 33.8709, 10197 = 33.8718, 10198 = 33.8729, 10199 = 33.8741, 10200 = 33.8753, 10201 = 33.8764, 10202 = 33.8773, 10203 = 33.8785, 10204 = 33.8796, 10205 = 33.8808, 10206 = 33.8819, 10207 = 33.8831, 10208 = 33.884, 10209 = 33.8851, 10210 = 33.8863, 10211 = 33.8875, 10212 = 33.8886, 10213 = 33.8895, 10214 = 33.8907, 10215 = 33.8918, 10216 = 33.893, 10217 = 33.8941, 10218 = 33.895, 10219 = 33.8962, 10220 = 33.8973, 10221 = 33.8985, 10222 = 33.8996, 10223 = 33.9005, 10224 = 33.9017, 10225 = 33.9028, 10226 = 33.904, 10227 = 33.9052, 10228 = 33.9063, 10229 = 33.9072, 10230 = 33.9083, 10231 = 33.9095, 10232 = 33.9107, 10233 = 33.9118, 10234 = 33.9127, 10235 = 33.9139, 10236 = 33.915, 10237 = 33.9162, 10238 = 33.9173, 10239 = 33.9182, 10240 = 33.9194, 10241 = 33.9205, 10242 = 33.9217, 10243 = 33.9228, 10244 = 33.924, 10245 = 33.9249, 10246 = 33.926, 10247 = 33.9272, 10248 = 33.9283, 10249 = 33.9295, 10250 = 33.9304, 10251 = 33.9315, 10252 = 33.9327, 10253 = 33.9338, 10254 = 33.935, 10255 = 33.9359, 10256 = 33.937, 10257 = 33.9382, 10258 = 33.9393, 10259 = 33.9405, 10260 = 33.9417, 10261 = 33.9425, 10262 = 33.9437, 10263 = 33.9448, 10264 = 33.946, 10265 = 33.9472, 10266 = 33.948, 10267 = 33.9492, 10268 = 33.9503, 10269 = 33.9515, 10270 = 33.9526, 10271 = 33.9535, 10272 = 33.9547, 10273 = 33.9558, 10274 = 33.957, 10275 = 33.9581, 10276 = 33.959, 10277 = 33.9602, 10278 = 33.9613, 10279 = 33.9625, 10280 = 33.9636, 10281 = 33.9648, 10282 = 33.9657, 10283 = 33.9668, 10284 = 33.968, 10285 = 33.9691, 10286 = 33.9703, 10287 = 33.9711, 10288 = 33.9723, 10289 = 33.9734, 10290 = 33.9746, 10291 = 33.9758, 10292 = 33.9766, 10293 = 33.9778, 10294 = 33.9789, 10295 = 33.9801, 10296 = 33.9812, 10297 = 33.9824, 10298 = 33.9833, 10299 = 33.9844, 10300 = 33.9856, 10301 = 33.9867, 10302 = 33.9879, 10303 = 33.9888, 10304 = 33.9899, 10305 = 33.9911, 10306 = 33.9922, 10307 = 33.9934, 10308 = 33.9942, 10309 = 33.9954, 10310 = 33.9965, 10311 = 33.9977, 10312 = 33.9988, 10313 = 33.9997, 10314 = 34.0009, 10315 = 34.002, 10316 = 34.0032, 10317 = 34.0043, 10318 = 34.0055, 10319 = 34.0063, 10320 = 34.0075, 10321 = 34.0086, 10322 = 34.0098, 10323 = 34.011, 10324 = 34.0118, 10325 = 34.013, 10326 = 34.0141, 10327 = 34.0153, 10328 = 34.0164, 10329 = 34.0173, 10330 = 34.0184, 10331 = 34.0196, 10332 = 34.0207, 10333 = 34.0219, 10334 = 34.0231, 10335 = 34.0239, 10336 = 34.0251, 10337 = 34.0262, 10338 = 34.0274, 10339 = 34.0285, 10340 = 34.0294, 10341 = 34.0305, 10342 = 34.0317, 10343 = 34.0328, 10344 = 34.034, 10345 = 34.0349, 10346 = 34.036, 10347 = 34.0372, 10348 = 34.0383, 10349 = 34.0395, 10350 = 34.0406, 10351 = 34.0415, 10352 = 34.0426, 10353 = 34.0438, 10354 = 34.0449, 10355 = 34.0461, 10356 = 34.0469, 10357 = 34.0481, 10358 = 34.0492, 10359 = 34.0504, 10360 = 34.0515, 10361 = 34.0524, 10362 = 34.0536, 10363 = 34.0547, 10364 = 34.0558, 10365 = 34.057, 10366 = 34.0579, 10367 = 34.059, 10368 = 34.0602, 10369 = 34.0613, 10370 = 34.0625, 10371 = 34.0636, 10372 = 34.0645, 10373 = 34.0656, 10374 = 34.0668, 10375 = 34.0679, 10376 = 34.0691, 10377 = 34.0699, 10378 = 34.0711, 10379 = 34.0722, 10380 = 34.0734, 10381 = 34.0745, 10382 = 34.0754, 10383 = 34.0765, 10384 = 34.0777, 10385 = 34.0788, 10386 = 34.08, 10387 = 34.0811, 10388 = 34.082, 10389 = 34.0831, 10390 = 34.0843, 10391 = 34.0854, 10392 = 34.0866, 10393 = 34.0874, 10394 = 34.0886, 10395 = 34.0897, 10396 = 34.0909, 10397 = 34.092, 10398 = 34.0929, 10399 = 34.094, 10400 = 34.0952, 10401 = 34.0963, 10402 = 34.0975, 10403 = 34.0983, 10404 = 34.0995, 10405 = 34.1006, 10406 = 34.1018, 10407 = 34.1029, 10408 = 34.1041, 10409 = 34.1049, 10410 = 34.1061, 10411 = 34.1072, 10412 = 34.1084, 10413 = 34.1095, 10414 = 34.1104, 10415 = 34.1115, 10416 = 34.1127, 10417 = 34.1138, 10418 = 34.115, 10419 = 34.1158, 10420 = 34.117, 10421 = 34.1181, 10422 = 34.1192, 10423 = 34.1204, 10424 = 34.1215, 10425 = 34.1224, 10426 = 34.1235, 10427 = 34.1247, 10428 = 34.1258, 10429 = 34.127, 10430 = 34.1278, 10431 = 34.129, 10432 = 34.1301, 10433 = 34.1313, 10434 = 34.1324, 10435 = 34.1333, 10436 = 34.1344, 10437 = 34.1356, 10438 = 34.1367, 10439 = 34.1378, 10440 = 34.139, 10441 = 34.1399, 10442 = 34.141, 10443 = 34.1421, 10444 = 34.1433, 10445 = 34.1444, 10446 = 34.1453, 10447 = 34.1464, 10448 = 34.1476, 10449 = 34.1487, 10450 = 34.1499, 10451 = 34.1507, 10452 = 34.1519, 10453 = 34.153, 10454 = 34.1541, 10455 = 34.1553, 10456 = 34.1561, 10457 = 34.1573, 10458 = 34.1584, 10459 = 34.1596, 10460 = 34.1607, 10461 = 34.1619, 10462 = 34.1627, 10463 = 34.1639, 10464 = 34.165, 10465 = 34.1661, 10466 = 34.1673, 10467 = 34.1681, 10468 = 34.1693, 10469 = 34.1704, 10470 = 34.1716, 10471 = 34.1727, 10472 = 34.1736, 10473 = 34.1747, 10474 = 34.1758, 10475 = 34.177, 10476 = 34.1781, 10477 = 34.1793, 10478 = 34.1801, 10479 = 34.1813, 10480 = 34.1824, 10481 = 34.1836, 10482 = 34.1847, 10483 = 34.1855, 10484 = 34.1867, 10485 = 34.1878, 10486 = 34.189, 10487 = 34.1901, 10488 = 34.191, 10489 = 34.1921, 10490 = 34.1932, 10491 = 34.1944, 10492 = 34.1955, 10493 = 34.1964, 10494 = 34.1975, 10495 = 34.1987, 10496 = 34.1998, 10497 = 34.2009, 10498 = 34.2021, 10499 = 34.2029, 10500 = 34.2041, 10501 = 34.2052, 10502 = 34.2064, 10503 = 34.2075, 10504 = 34.2084, 10505 = 34.2095, 10506 = 34.2106, 10507 = 34.2118, 10508 = 34.2129, 10509 = 34.2138, 10510 = 34.2149, 10511 = 34.216, 10512 = 34.2172, 10513 = 34.2183, 10514 = 34.2195, 10515 = 34.2203, 10516 = 34.2215, 10517 = 34.2226, 10518 = 34.2237, 10519 = 34.2249, 10520 = 34.2257, 10521 = 34.2269, 10522 = 34.228, 10523 = 34.2291, 10524 = 34.2303, 10525 = 34.2311, 10526 = 34.2323, 10527 = 34.2334, 10528 = 34.2345, 10529 = 34.2357, 10530 = 34.2368, 10531 = 34.2377, 10532 = 34.2388, 10533 = 34.2399, 10534 = 34.2411, 10535 = 34.2422, 10536 = 34.2431, 10537 = 34.2442, 10538 = 34.2453, 10539 = 34.2465, 10540 = 34.2476, 10541 = 34.2485, 10542 = 34.2496, 10543 = 34.2507, 10544 = 34.2519, 10545 = 34.253, 10546 = 34.2539, 10547 = 34.255, 10548 = 34.2561, 10549 = 34.2573, 10550 = 34.2584, 10551 = 34.2595, 10552 = 34.2604, 10553 = 34.2615, 10554 = 34.2627, 10555 = 34.2638, 10556 = 34.2649, 10557 = 34.2658, 10558 = 34.2669, 10559 = 34.2681, 10560 = 34.2692, 10561 = 34.2703, 10562 = 34.2712, 10563 = 34.2723, 10564 = 34.2735, 10565 = 34.2746, 10566 = 34.2757, 10567 = 34.2769, 10568 = 34.2777, 10569 = 34.2789, 10570 = 34.28, 10571 = 34.2811, 10572 = 34.2823, 10573 = 34.2831, 10574 = 34.2842, 10575 = 34.2854, 10576 = 34.2865, 10577 = 34.2876, 10578 = 34.2885, 10579 = 34.2896, 10580 = 34.2908, 10581 = 34.2919, 10582 = 34.293, 10583 = 34.2939, 10584 = 34.295, 10585 = 34.2961, 10586 = 34.2973, 10587 = 34.2984, 10588 = 34.2995, 10589 = 34.3004, 10590 = 34.3015, 10591 = 34.3027, 10592 = 34.3038, 10593 = 34.3049, 10594 = 34.3058, 10595 = 34.3069, 10596 = 34.308, 10597 = 34.3092, 10598 = 34.3103, 10599 = 34.3112, 10600 = 34.3123, 10601 = 34.3134, 10602 = 34.3146, 10603 = 34.3157, 10604 = 34.3168, 10605 = 34.3177, 10606 = 34.3188, 10607 = 34.3199, 10608 = 34.3211, 10609 = 34.3222, 10610 = 34.323, 10611 = 34.3242, 10612 = 34.3253, 10613 = 34.3264, 10614 = 34.3276, 10615 = 34.3284, 10616 = 34.3296, 10617 = 34.3307, 10618 = 34.3318, 10619 = 34.3329, 10620 = 34.3341, 10621 = 34.3349, 10622 = 34.3361, 10623 = 34.3372, 10624 = 34.3383, 10625 = 34.3394, 10626 = 34.3403, 10627 = 34.3414, 10628 = 34.3426, 10629 = 34.3437, 10630 = 34.3448, 10631 = 34.3457, 10632 = 34.3468, 10633 = 34.3479, 10634 = 34.3491, 10635 = 34.3502, 10636 = 34.351, 10637 = 34.3522, 10638 = 34.3533, 10639 = 34.3544, 10640 = 34.3556, 10641 = 34.3567, 10642 = 34.3575, 10643 = 34.3587, 10644 = 34.3598, 10645 = 34.3609, 10646 = 34.362, 10647 = 34.3629, 10648 = 34.364, 10649 = 34.3652, 10650 = 34.3663, 10651 = 34.3674, 10652 = 34.3683, 10653 = 34.3694, 10654 = 34.3705, 10655 = 34.3716, 10656 = 34.3728, 10657 = 34.3739, 10658 = 34.3747, 10659 = 34.3759, 10660 = 34.377, 10661 = 34.3781, 10662 = 34.3793, 10663 = 34.3801, 10664 = 34.3812, 10665 = 34.3824, 10666 = 34.3835, 10667 = 34.3846, 10668 = 34.3855, 10669 = 34.3866, 10670 = 34.3877, 10671 = 34.3888, 10672 = 34.39, 10673 = 34.3908, 10674 = 34.3919, 10675 = 34.3931, 10676 = 34.3942, 10677 = 34.3953, 10678 = 34.3965, 10679 = 34.3973, 10680 = 34.3984, 10681 = 34.3996, 10682 = 34.4007, 10683 = 34.4018, 10684 = 34.4027, 10685 = 34.4038, 10686 = 34.4049, 10687 = 34.406, 10688 = 34.4072, 10689 = 34.408, 10690 = 34.4091, 10691 = 34.4103, 10692 = 34.4114, 10693 = 34.4125, 10694 = 34.4136, 10695 = 34.4145, 10696 = 34.4156, 10697 = 34.4167, 10698 = 34.4179, 10699 = 34.419, 10700 = 34.4198, 10701 = 34.4209, 10702 = 34.4221, 10703 = 34.4232, 10704 = 34.4243, 10705 = 34.4252, 10706 = 34.4263, 10707 = 34.4274, 10708 = 34.4285, 10709 = 34.4297, 10710 = 34.4308, 10711 = 34.4316, 10712 = 34.4328, 10713 = 34.4339, 10714 = 34.435, 10715 = 34.4361, 10716 = 34.437, 10717 = 34.4381, 10718 = 34.4392, 10719 = 34.4403, 10720 = 34.4415, 10721 = 34.4423, 10722 = 34.4434, 10723 = 34.4446, 10724 = 34.4457, 10725 = 34.4468, 10726 = 34.4477, 10727 = 34.4488, 10728 = 34.4499, 10729 = 34.451, 10730 = 34.4521, 10731 = 34.4533, 10732 = 34.4541, 10733 = 34.4552, 10734 = 34.4564, 10735 = 34.4575, 10736 = 34.4586, 10737 = 34.4594, 10738 = 34.4606, 10739 = 34.4617, 10740 = 34.4628, 10741 = 34.4639, 10742 = 34.4648, 10743 = 34.4659, 10744 = 34.467, 10745 = 34.4682, 10746 = 34.4693, 10747 = 34.4704, 10748 = 34.4712, 10749 = 34.4724, 10750 = 34.4735, 10751 = 34.4746, 10752 = 34.4757, 10753 = 34.4766, 10754 = 34.4777, 10755 = 34.4788, 10756 = 34.4799, 10757 = 34.4811, 10758 = 34.4819, 10759 = 34.483, 10760 = 34.4841, 10761 = 34.4853, 10762 = 34.4864, 10763 = 34.4872, 10764 = 34.4883, 10765 = 34.4895, 10766 = 34.4906, 10767 = 34.4917, 10768 = 34.4928, 10769 = 34.4937, 10770 = 34.4948, 10771 = 34.4959, 10772 = 34.497, 10773 = 34.4981, 10774 = 34.499, 10775 = 34.5001, 10776 = 34.5012, 10777 = 34.5023, 10778 = 34.5035, 10779 = 34.5043, 10780 = 34.5054, 10781 = 34.5065, 10782 = 34.5077, 10783 = 34.5088, 10784 = 34.5099, 10785 = 34.5107, 10786 = 34.5119, 10787 = 34.513, 10788 = 34.5141, 10789 = 34.5152, 10790 = 34.5161, 10791 = 34.5172, 10792 = 34.5183, 10793 = 34.5194, 10794 = 34.5205, 10795 = 34.5214, 10796 = 34.5225, 10797 = 34.5236, 10798 = 34.5247, 10799 = 34.5259, 10800 = 34.527, 10801 = 34.5278, 10802 = 34.5289, 10803 = 34.53, 10804 = 34.5312, 10805 = 34.5323, 10806 = 34.5331, 10807 = 34.5342, 10808 = 34.5354, 10809 = 34.5365, 10810 = 34.5376, 10811 = 34.5384, 10812 = 34.5395, 10813 = 34.5407, 10814 = 34.5418, 10815 = 34.5429, 10816 = 34.5437, 10817 = 34.5449, 10818 = 34.546, 10819 = 34.5471, 10820 = 34.5482, 10821 = 34.5493, 10822 = 34.5502, 10823 = 34.5513, 10824 = 34.5524, 10825 = 34.5535, 10826 = 34.5546, 10827 = 34.5555, 10828 = 34.5566, 10829 = 34.5577, 10830 = 34.5588, 10831 = 34.5599, 10832 = 34.5608, 10833 = 34.5619, 10834 = 34.563, 10835 = 34.5641, 10836 = 34.5652, 10837 = 34.5663, 10838 = 34.5672, 10839 = 34.5683, 10840 = 34.5694, 10841 = 34.5705, 10842 = 34.5717, 10843 = 34.5725, 10844 = 34.5736, 10845 = 34.5747, 10846 = 34.5758, 10847 = 34.5769, 10848 = 34.5778, 10849 = 34.5789, 10850 = 34.58, 10851 = 34.5811, 10852 = 34.5822, 10853 = 34.5831, 10854 = 34.5842, 10855 = 34.5853, 10856 = 34.5864, 10857 = 34.5875, 10858 = 34.5887, 10859 = 34.5895, 10860 = 34.5906, 10861 = 34.5917, 10862 = 34.5928, 10863 = 34.5939, 10864 = 34.5948, 10865 = 34.5959, 10866 = 34.597, 10867 = 34.5981, 10868 = 34.5992, 10869 = 34.6001, 10870 = 34.6012, 10871 = 34.6023, 10872 = 34.6034, 10873 = 34.6045, 10874 = 34.6056, 10875 = 34.6065, 10876 = 34.6076, 10877 = 34.6087, 10878 = 34.6098, 10879 = 34.6109, 10880 = 34.6118, 10881 = 34.6129, 10882 = 34.614, 10883 = 34.6151, 10884 = 34.6162, 10885 = 34.6171, 10886 = 34.6182, 10887 = 34.6193, 10888 = 34.6204, 10889 = 34.6215, 10890 = 34.6226, 10891 = 34.6234, 10892 = 34.6246, 10893 = 34.6257, 10894 = 34.6268, 10895 = 34.6279, 10896 = 34.6287, 10897 = 34.6298, 10898 = 34.631, 10899 = 34.6321, 10900 = 34.6332, 10901 = 34.634, 10902 = 34.6351, 10903 = 34.6362, 10904 = 34.6373, 10905 = 34.6385, 10906 = 34.6393, 10907 = 34.6404, 10908 = 34.6415, 10909 = 34.6426, 10910 = 34.6437, 10911 = 34.6448, 10912 = 34.6457, 10913 = 34.6468, 10914 = 34.6479, 10915 = 34.649, 10916 = 34.6501, 10917 = 34.651, 10918 = 34.6521, 10919 = 34.6532, 10920 = 34.6543, 10921 = 34.6554, 10922 = 34.6562, 10923 = 34.6573, 10924 = 34.6584, 10925 = 34.6596, 10926 = 34.6607, 10927 = 34.6618, 10928 = 34.6626, 10929 = 34.6637, 10930 = 34.6648, 10931 = 34.6659, 10932 = 34.667, 10933 = 34.6679, 10934 = 34.669, 10935 = 34.6701, 10936 = 34.6712, 10937 = 34.6723, 10938 = 34.6731, 10939 = 34.6743, 10940 = 34.6754, 10941 = 34.6765, 10942 = 34.6776, 10943 = 34.6784, 10944 = 34.6795, 10945 = 34.6806, 10946 = 34.6817, 10947 = 34.6828, 10948 = 34.684, 10949 = 34.6848, 10950 = 34.6859, 10951 = 34.687, 10952 = 34.6881, 10953 = 34.6892, 10954 = 34.6901, 10955 = 34.6912, 10956 = 34.6923, 10957 = 34.6934, 10958 = 34.6945, 10959 = 34.6953, 10960 = 34.6964, 10961 = 34.6975, 10962 = 34.6986, 10963 = 34.6997, 10964 = 34.7009, 10965 = 34.7017, 10966 = 34.7028, 10967 = 34.7039, 10968 = 34.705, 10969 = 34.7061, 10970 = 34.7069, 10971 = 34.708, 10972 = 34.7092, 10973 = 34.7103, 10974 = 34.7114, 10975 = 34.7122, 10976 = 34.7133, 10977 = 34.7144, 10978 = 34.7155, 10979 = 34.7166, 10980 = 34.7177, 10981 = 34.7186, 10982 = 34.7197, 10983 = 34.7208, 10984 = 34.7219, 10985 = 34.723, 10986 = 34.7238, 10987 = 34.7249, 10988 = 34.726, 10989 = 34.7271, 10990 = 34.7282, 10991 = 34.7291, 10992 = 34.7302, 10993 = 34.7313, 10994 = 34.7324, 10995 = 34.7335, 10996 = 34.7343, 10997 = 34.7354, 10998 = 34.7365, 10999 = 34.7376, 11000 = 34.7387, 11001 = 34.7398, 11002 = 34.7407, 11003 = 34.7418, 11004 = 34.7429, 11005 = 34.744, 11006 = 34.7451, 11007 = 34.7459, 11008 = 34.747, 11009 = 34.7481, 11010 = 34.7492, 11011 = 34.7503, 11012 = 34.7512, 11013 = 34.7523, 11014 = 34.7534, 11015 = 34.7545, 11016 = 34.7556, 11017 = 34.7567, 11018 = 34.7575, 11019 = 34.7586, 11020 = 34.7597, 11021 = 34.7608, 11022 = 34.7619, 11023 = 34.7627, 11024 = 34.7639, 11025 = 34.765, 11026 = 34.7661, 11027 = 34.7672, 11028 = 34.768, 11029 = 34.7691, 11030 = 34.7702, 11031 = 34.7713, 11032 = 34.7724, 11033 = 34.7732, 11034 = 34.7743, 11035 = 34.7754, 11036 = 34.7765, 11037 = 34.7776, 11038 = 34.7787, 11039 = 34.7796, 11040 = 34.7807, 11041 = 34.7818, 11042 = 34.7829, 11043 = 34.784, 11044 = 34.7848, 11045 = 34.7859, 11046 = 34.787, 11047 = 34.7881, 11048 = 34.7892, 11049 = 34.79, 11050 = 34.7911, 11051 = 34.7922, 11052 = 34.7933, 11053 = 34.7944, 11054 = 34.7955, 11055 = 34.7964, 11056 = 34.7975, 11057 = 34.7986, 11058 = 34.7997, 11059 = 34.8008, 11060 = 34.8016, 11061 = 34.8027, 11062 = 34.8038, 11063 = 34.8049, 11064 = 34.806, 11065 = 34.8068, 11066 = 34.8079, 11067 = 34.809, 11068 = 34.8101, 11069 = 34.8112, 11070 = 34.8123, 11071 = 34.8132, 11072 = 34.8143, 11073 = 34.8154, 11074 = 34.8165, 11075 = 34.8176, 11076 = 34.8184, 11077 = 34.8195, 11078 = 34.8206, 11079 = 34.8217, 11080 = 34.8228, 11081 = 34.8236, 11082 = 34.8247, 11083 = 34.8258, 11084 = 34.8269, 11085 = 34.828, 11086 = 34.8288, 11087 = 34.8299, 11088 = 34.831, 11089 = 34.8321, 11090 = 34.8332, 11091 = 34.8343, 11092 = 34.8351, 11093 = 34.8362, 11094 = 34.8373, 11095 = 34.8384, 11096 = 34.8395, 11097 = 34.8404, 11098 = 34.8415, 11099 = 34.8426, 11100 = 34.8437, 11101 = 34.8448, 11102 = 34.8456, 11103 = 34.8467, 11104 = 34.8478, 11105 = 34.8489, 11106 = 34.85, 11107 = 34.8511, 11108 = 34.8519, 11109 = 34.853, 11110 = 34.8541, 11111 = 34.8552, 11112 = 34.8563, 11113 = 34.8571, 11114 = 34.8582, 11115 = 34.8593, 11116 = 34.8604, 11117 = 34.8615, 11118 = 34.8623, 11119 = 34.8634, 11120 = 34.8645, 11121 = 34.8656, 11122 = 34.8667, 11123 = 34.8675, 11124 = 34.8686, 11125 = 34.8697, 11126 = 34.8708, 11127 = 34.8719, 11128 = 34.873, 11129 = 34.8738, 11130 = 34.8749, 11131 = 34.876, 11132 = 34.8771, 11133 = 34.8782, 11134 = 34.879, 11135 = 34.8801, 11136 = 34.8812, 11137 = 34.8823, 11138 = 34.8834, 11139 = 34.8842, 11140 = 34.8853, 11141 = 34.8864, 11142 = 34.8875, 11143 = 34.8886, 11144 = 34.8897, 11145 = 34.8905, 11146 = 34.8916, 11147 = 34.8927, 11148 = 34.8938, 11149 = 34.8949, 11150 = 34.8957, 11151 = 34.8968, 11152 = 34.8979, 11153 = 34.899, 11154 = 34.9001, 11155 = 34.9009, 11156 = 34.902, 11157 = 34.9031, 11158 = 34.9042, 11159 = 34.9053, 11160 = 34.9064, 11161 = 34.9072, 11162 = 34.9083, 11163 = 34.9094, 11164 = 34.9105, 11165 = 34.9116, 11166 = 34.9124, 11167 = 34.9135, 11168 = 34.9146, 11169 = 34.9157, 11170 = 34.9168, 11171 = 34.9176, 11172 = 34.9187, 11173 = 34.9198, 11174 = 34.9209, 11175 = 34.922, 11176 = 34.9228, 11177 = 34.9239, 11178 = 34.925, 11179 = 34.9261, 11180 = 34.9272, 11181 = 34.9283, 11182 = 34.9291, 11183 = 34.9302, 11184 = 34.9313, 11185 = 34.9324, 11186 = 34.9335, 11187 = 34.9343, 11188 = 34.9354, 11189 = 34.9365, 11190 = 34.9376, 11191 = 34.9387, 11192 = 34.9395, 11193 = 34.9406, 11194 = 34.9417, 11195 = 34.9428, 11196 = 34.9439, 11197 = 34.9449, 11198 = 34.9458, 11199 = 34.9469, 11200 = 34.9479, 11201 = 34.949, 11202 = 34.9501, 11203 = 34.951, 11204 = 34.952, 11205 = 34.9531, 11206 = 34.9542, 11207 = 34.9553, 11208 = 34.9561, 11209 = 34.9572, 11210 = 34.9583, 11211 = 34.9594, 11212 = 34.9605, 11213 = 34.9613, 11214 = 34.9624, 11215 = 34.9635, 11216 = 34.9646, 11217 = 34.9657, 11218 = 34.9668, 11219 = 34.9676, 11220 = 34.9687, 11221 = 34.9698, 11222 = 34.9709, 11223 = 34.972, 11224 = 34.9728, 11225 = 34.9739, 11226 = 34.9749, 11227 = 34.976, 11228 = 34.9771, 11229 = 34.9779, 11230 = 34.979, 11231 = 34.9801, 11232 = 34.9812, 11233 = 34.9823, 11234 = 34.9834, 11235 = 34.9842, 11236 = 34.9853, 11237 = 34.9864, 11238 = 34.9875, 11239 = 34.9886, 11240 = 34.9894, 11241 = 34.9905, 11242 = 34.9916, 11243 = 34.9927, 11244 = 34.9937, 11245 = 34.9946, 11246 = 34.9956, 11247 = 34.9967, 11248 = 34.9978, 11249 = 34.9989, 11250 = 35 Trvalo to asi 35 sekund

2 roky  2 Likes
#1
V jakém programu to je ?

#2
A do listu, který bude odevzdávat napíšete, že vám výsledek vygeneroval počítač ??

2 roky  1 Like
#7
Www
no ano a mikrosekundu by trvalo vyskusat 13 cisel ci vyhovuje.... resp. 4 minuty na kalkulacce

#8
Žák
Jde to samozřejmně i pomocí rovnic a úvah. Kdo chce ale dělat MO by na tohle měl přijít sám.

2 roky  1 Like
#9
žák
Takže matematický vzorec pro tuto úlohu neexistuje ??

#10
žák
Počítal jsem takto:
x + x/2 + x + x/5 + x + x/9 = y³ (- na třetí)
343/90 = y³             / *90
343x = y³ * 90         / ³√ (- třetí odmocnina)
3,81x =³√ (y³ * 90)
x = (³√ (y * 90)) / 3,81
A jak teď zjistit "x", pokud na druhé straně mám další nevyjádřenou... ?

#1
nebo si můžeš x vyjádřit jako x=(y³*90)/343

#11
Pomocník
Hledáte nejnižší pětimístné číslo a máte určit nejmenší číslo, které si Katka mohla myslet, to číslo musí být na třetí, takže můžete zkoušet, třeba 203=8000, stále není pětimístné, tak zkusíte 213=9261, potom zkusíte 223=10648, to je nejnižší pětimístné číslo na třetí, takže odpověď je 22, nikoli 35.

2 roky  1 Like
#1
Ale to číslo na konci není to číslo, které si katka myslela - na třetí, je to jiné přirození číslo na třetí.

#12
Žák
Když ale do řádků dosadíš 10648 tak ti výjde 40580,7111 - má být přirozené. Pak by jste nenašel 3odmocninu přirozenou.

#13
Žák
Vážení, jestli chápu správně zadání, tak "n" nemůže být 11250, protože to má být součet, což by v tomto případě bylo 9.
takže bych to viděl na "x + n/2" v prvním řádku.

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