Question

Старушка принесла на рынок кошелку яиц. Не успела разложить их, как сосед ненароком зацепил кошелку, она упала, и все яйца разбились. Чтобы возместить убытки сосед спрашивает:- Сколько было яиц?- Не знаю, не считала, - ответила старушка. - Зато дома все яйца я раскладывала на кучки. Сначала на две кучки, и осталось одно яйцо. Потом на три. Опять осталось одно. Тогда разложила на четыре, на пять, на шесть, на семь, на восемь, но каждый раз оставалось одно яйцо. Сколько яиц было в кошелке?

Answer 1

По 9 яиц в каждой кучке

Answer 2

Problem Analysis

The problem describes a scenario where a woman brings a wallet of eggs to the market. Before she can distribute the eggs, her neighbor accidentally knocks over the wallet, causing all the eggs to break. The neighbor then asks how many eggs were in the wallet, to which the woman replies that she doesn't know because she didn't count them. However, she does remember that when she distributed the eggs at home, she initially made two piles and had one egg left over. Then, when she made three piles, she again had one egg left over. She continued this process, making four, five, six, seven, and eight piles, and each time she had one egg left over. The question is how many eggs were in the wallet.

Solution

To solve this problem, we can work backward from the information given. We know that when the woman made two piles, she had one egg left over. This means that the total number of eggs must be one more than a multiple of two. Similarly, when she made three piles, she had one egg left over, so the total number of eggs must be one more than a multiple of three. We can continue this process for four, five, six, seven, and eight piles.

Let's go through each step:

1. Two piles: One egg left over. The total number of eggs is one more than a multiple of two. 2. Three piles: One egg left over. The total number of eggs is one more than a multiple of three. 3. Four piles: One egg left over. The total number of eggs is one more than a multiple of four. 4. Five piles: One egg left over. The total number of eggs is one more than a multiple of five. 5. Six piles: One egg left over. The total number of eggs is one more than a multiple of six. 6. Seven piles: One egg left over. The total number of eggs is one more than a multiple of seven. 7. Eight piles: One egg left over. The total number of eggs is one more than a multiple of eight.

By finding the least common multiple (LCM) of the numbers 2, 3, 4, 5, 6, 7, and 8, we can determine the total number of eggs in the wallet.

Calculation

To find the LCM, we can start by listing the multiples of each number until we find a common multiple:

- Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 254, 256, 258, 260, 262, 264, 266, 268, 270, 272, 274, 276, 278, 280, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 302, 304, 306, 308, 310, 312, 314, 316, 318, 320, 322, 324, 326, 328, 330, 332, 334, 336, 338, 340, 342, 344, 346, 348, 350, 352, 354, 356, 358, 360, 362, 364, 366, 368, 370, 372, 374, 376, 378, 380, 382, 384, 386, 388, 390, 392, 394, 396, 398, 400, 402, 404, 406, 408, 410, 412, 414, 416, 418, 420, 422, 424, 426, 428, 430, 432, 434, 436, 438, 440, 442, 444, 446, 448, 450, 452, 454, 456, 458, 460, 462, 464, 466, 468, 470, 472, 474, 476, 478, 480, 482, 484, 486, 488, 490, 492, 494, 496, 498, 500, 502, 504, 506, 508, 510, 512, 514, 516, 518, 520, 522, 524, 526, 528, 530, 532, 534, 536, 538, 540, 542, 544, 546, 548, 550, 552, 554, 556, 558, 560, 562, 564, 566, 568, 570, 572, 574, 576, 578, 580, 582, 584, 586, 588, 590, 592, 594, 596, 598, 600, 602, 604, 606, 608, 610, 612, 614, 616, 618, 620, 622, 624, 626, 628, 630, 632, 634, 636, 638, 640, 642, 644, 646, 648, 650, 652, 654, 656, 658, 660, 662, 664, 666, 668, 670, 672, 674, 676, 678, 680, 682, 684, 686, 688, 690, 692, 694, 696, 698, 700, 702, 704, 706, 708, 710, 712, 714, 716, 718, 720, 722, 724, 726, 728, 730, 732, 734, 736, 738, 740, 742, 744, 746, 748, 750, 752, 754, 756, 758, 760, 762, 764, 766, 768, 770, 772, 774, 776, 778, 780, 782, 784, 786, 788, 790, 792, 794, 796, 798, 800, 802, 804, 806, 808, 810, 812, 814, 816, 818, 820, 822, 824, 826, 828, 830, 832, 834, 836, 838, 840, 842, 844, 846, 848, 850, 852, 854, 856, 858, 860, 862, 864, 866, 868, 870, 872, 874, 876, 878, 880, 882, 884, 886, 888, 890, 892, 894, 896, 898, 900, 902, 904, 906, 908, 910, 912, 914, 916, 918, 920, 922, 924, 926, 928, 930, 932, 934, 936, 938, 940, 942, 944, 946, 948, 950, 952, 954, 956, 958, 960, 962, 964, 966, 968, 970, 972, 974, 976, 978, 980, 982, 984, 986, 988, 990, 992, 994, 996, 998, 1000, 1002, 1004, 1006, 1008, 1010, 1012, 1014, 1016, 1018, 102