Question

Начальное число 96. Волшебный калькулятор имеет кнопку при нажатии на которую прибавляется сумма цифр числа. Эта кнопка была нажата много раз. Могло ли встретиться в полученных суммах число 9333.

Answer 1

Мне кажется ,что нет,но я не уверенна. Я из 9333 отняла 96 получила 9237. Потом нашла сумму слагаемых (9 и 6 равно 15). Разделила 9237 на 15 и получила не целое число. А поскольку к 96 надо прибавить сумму слагаемых (15) много раз ,а число при делении получилось не целое, то такое число встретиться не могло

Answer 2

The Magic Calculator and the Number 9333

The magic calculator is a device that adds up the sum of the digits of a given number when a specific button is pressed. In this case, we start with the number 96 and repeatedly press the button to obtain a series of sums. The question is whether the number 9333 could appear in the resulting sums.

To answer this question, let's analyze the process step by step.

1. Starting with the number 96, we calculate the sum of its digits: 9 + 6 = 15. 2. We then add the resulting sum to the original number: 96 + 15 = 111. 3. Next, we calculate the sum of the digits of 111: 1 + 1 + 1 = 3. 4. We add the sum to the previous result: 111 + 3 = 114. 5. We continue this process, calculating the sum of the digits and adding it to the previous result, until we reach a certain number of iterations.

Now, let's determine if the number 9333 can be obtained through this process.

Starting with 96, we can calculate the sums as follows:

- 96 + 15 = 111 - 111 + 3 = 114 - 114 + 6 = 120 - 120 + 3 = 123 - 123 + 6 = 129 - 129 + 12 = 141 - 141 + 6 = 147 - 147 + 12 = 159 - 159 + 15 = 174 - 174 + 12 = 186 - 186 + 15 = 201 - 201 + 3 = 204 - 204 + 6 = 210 - 210 + 3 = 213 - 213 + 6 = 219 - 219 + 12 = 231 - 231 + 6 = 237 - 237 + 12 = 249 - 249 + 15 = 264 - 264 + 12 = 276 - 276 + 15 = 291 - 291 + 3 = 294 - 294 + 6 = 300 - 300 + 3 = 303 - 303 + 6 = 309 - 309 + 12 = 321 - 321 + 6 = 327 - 327 + 12 = 339 - 339 + 15 = 354 - 354 + 12 = 366 - 366 + 15 = 381 - 381 + 3 = 384 - 384 + 6 = 390 - 390 + 3 = 393 - 393 + 6 = 399 - 399 + 12 = 411 - 411 + 6 = 417 - 417 + 12 = 429 - 429 + 15 = 444 - 444 + 12 = 456 - 456 + 15 = 471 - 471 + 3 = 474 - 474 + 6 = 480 - 480 + 3 = 483 - 483 + 6 = 489 - 489 + 12 = 501 - 501 + 6 = 507 - 507 + 12 = 519 - 519 + 15 = 534 - 534 + 12 = 546 - 546 + 15 = 561 - 561 + 3 = 564 - 564 + 6 = 570 - 570 + 3 = 573 - 573 + 6 = 579 - 579 + 12 = 591 - 591 + 6 = 597 - 597 + 12 = 609 - 609 + 15 = 624 - 624 + 12 = 636 - 636 + 15 = 651 - 651 + 3 = 654 - 654 + 6 = 660 - 660 + 3 = 663 - 663 + 6 = 669 - 669 + 12 = 681 - 681 + 6 = 687 - 687 + 12 = 699 - 699 + 15 = 714 - 714 + 12 = 726 - 726 + 15 = 741 - 741 + 3 = 744 - 744 + 6 = 750 - 750 + 3 = 753 - 753 + 6 = 759 - 759 + 12 = 771 - 771 + 6 = 777 - 777 + 12 = 789 - 789 + 15 = 804 - 804 + 12 = 816 - 816 + 15 = 831 - 831 + 3 = 834 - 834 + 6 = 840 - 840 + 3 = 843 - 843 + 6 = 849 - 849 + 12 = 861 - 861 + 6 = 867 - 867 + 12 = 879 - 879 + 15 = 894 - 894 + 12 = 906 - 906 + 15 = 921 - 921 + 3 = 924 - 924 + 6 = 930 - 930 + 3 = 933 - 933 + 6 = 939 - 939 + 12 = 951 - 951 + 6 = 957 - 957 + 12 = 969 - 969 + 15 = 984 - 984 + 12 = 996 - 996 + 15 = 1011 - 1011 + 3 = 1014 - 1014 + 6 = 1020 - 1020 + 3 = 1023 - 1023 + 6 = 1029 - 1029 + 12 = 1041 - 1041 + 6 = 1047 - 1047 + 12 = 1059 - 1059 + 15 = 1074 - 1074 + 12 = 1086 - 1086 + 15 = 1101 - 1101 + 3 = 1104 - 1104 + 6 = 1110 - 1110 + 3 = 1113 - 1113 + 6 = 1119 - 1119 + 12 = 1131 - 1131 + 6 = 1137 - 1137 + 12 = 1149 - 1149 + 15 = 1164 - 1164 + 12 = 1176 - 1176 + 15 = 1191 - 1191 + 3 = 1194 - 1194 + 6 = 1200 - 1200 + 3 = 1203 - 1203 + 6 = 1209 - 1209 + 12 = 1221 - 1221 + 6 = 1227 - 1227 + 12 = 1239 - 1239 + 15 = 1254 - 1254 + 12 = 1266 - 1266 + 15 = 1281 - 1281 + 3 = 1284 - 1284 + 6 = 1290 - 1290 + 3 = 1293 - 1293 + 6 = 1299 - 1299 + 12 = 1311 - 1311 + 6 = 1317 - 1317 + 12 = 1329 - 1329 + 15 = 1344 - 1344 + 12 = 1356 - 1356 + 15 = 1371 - 1371 + 3 = 1374 - 1374 + 6 = 1380 - 1380 + 3 = 1383 - 1383 + 6 = 1389 - 1389 + 12 = 1401 - 1401 + 6 = 1407 - 1407 + 12 = 1419 - 1419 + 15 = 1434 - 1434 + 12 = 1446 - 1446 + 15 = 1461 - 1461 + 3 = 1464 - 1464 + 6 = 1470 - 1470 + 3 = 1473 - 1473 + 6 = 1479 - 1479 + 12 = 1491 - 1491 + 6 = 1497 - 1497 + 12 = 1509 - 1509 + 15 = 1524 - 1524 + 12 = 1536 - 1536 + 15 = 1551 - 1551 + 3 = 1554 - 1554 + 6 = 1560 - 1560 + 3 = 1563 - 1563 + 6 = 1569 - 1569 + 12 = 1581 - 1581 + 6 = 1587