Question

ДАЮ 40 БАЛЛОВ!!!!!!!!!!!!!! Написано 1992-ух значное число. Каждое двузначное число, образованное соседними цифрами, делится на 17 ИЛИ 23. Последняя цифра числа 1. Какова первая цифра числа. Можно с объяснением пж

Answer 1

Сначала рассмотрим все двузначные числа, делящиеся на 17 или 23:

17, 34, 51, 68, 85,

23, 46, 69, 92.

Замечаем, что у этих чисел последние цифры различны, поэтому , искомое число мы сможем восстановить однозначно.

Последняя цифра 1, значит, соответствующее двузначное чисто 51, т.е. предыдущая цифра в числе 5.

Цифра 5 соответствует двузначному числу 85, Поэтому перед ней стоит цифра 8.

Аналогично рассуждая, получим ряд из девяти последних цифр числа: 692346851.

Набор 92346 будет теперь всё время повторяться.

Всего цифр в этом числе 1992,

из них: 3 последние "851",

дальше перед ними повторяется период

из 5 цифр "92346"

то есть :

1992-3=1989 цифр на повторение периода

они будут повторяться

1989 :5=397 раз (4 в остатке)

раз осталось 4 в остатке, то

в начале числа будет четыре числа из периода, то есть "2346"

а значит первая цифра =2

ответ : 2

Answer 2

Ответ:

2

Объяснение:

Дано, что числа двузначные.

Кратные 17: 17-34-51-68-85

Кратные 23: 23-46-69-92

Как видно, последние 2 цифры большого числа это 51. Тогда перед ними стоит цифра 8.

Вырисовывается цикличная последовательность из имеющихся чисел:

69234692346851 с повтором цифр "69234"

Отнимаем 4 последних знака: 1992-4=1988

Делим на кол-во цифр в одном цикле: 1988/5=397 - полных циклов и еще 3 лишних цифры: 234. Первая цифра - 2.

Answer 3

Problem Analysis

We are given a 3-digit number written in the form of XY1, where X and Y are the first and second digits, respectively. We need to find the value of X. The given conditions are: - Every 2-digit number formed by the neighboring digits is divisible by either 17 or 23. - The last digit of the number is 1.

Solution

To find the value of X, we need to check which 2-digit numbers formed by the neighboring digits are divisible by either 17 or 23. Since the last digit is 1, we can ignore any 2-digit numbers ending in 0.

Let's analyze the possible values of XY1:

- X = 1: - In this case, the number is 11Y1. The only 2-digit number formed by the neighboring digits is 11, which is not divisible by either 17 or 23. Therefore, X cannot be 1.

- X = 2: - In this case, the number is 21Y1. The 2-digit numbers formed by the neighboring digits are 21 and 11. Let's check if they are divisible by either 17 or 23: - 21 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - Therefore, X cannot be 2.

- X = 3: - In this case, the number is 31Y1. The 2-digit numbers formed by the neighboring digits are 31 and 11. Let's check if they are divisible by either 17 or 23: - 31 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - Therefore, X cannot be 3.

- X = 4: - In this case, the number is 41Y1. The 2-digit numbers formed by the neighboring digits are 41, 11, and 14. Let's check if they are divisible by either 17 or 23: - 41 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - 14 is not divisible by either 17 or 23. - Therefore, X cannot be 4.

- X = 5: - In this case, the number is 51Y1. The 2-digit numbers formed by the neighboring digits are 51, 11, and 15. Let's check if they are divisible by either 17 or 23: - 51 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - 15 is not divisible by either 17 or 23. - Therefore, X cannot be 5.

- X = 6: - In this case, the number is 61Y1. The 2-digit numbers formed by the neighboring digits are 61, 11, and 16. Let's check if they are divisible by either 17 or 23: - 61 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - 16 is not divisible by either 17 or 23. - Therefore, X cannot be 6.

- X = 7: - In this case, the number is 71Y1. The 2-digit numbers formed by the neighboring digits are 71, 11, and 17. Let's check if they are divisible by either 17 or 23: - 71 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - 17 is divisible by 17. - Therefore, X can be 7.

- X = 8: - In this case, the number is 81Y1. The 2-digit numbers formed by the neighboring digits are 81, 11, and 18. Let's check if they are divisible by either 17 or 23: - 81 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - 18 is not divisible by either 17 or 23. - Therefore, X cannot be 8.

- X = 9: - In this case, the number is 91Y1. The 2-digit numbers formed by the neighboring digits are 91, 11, and 19. Let's check if they are divisible by either 17 or 23: - 91 is not divisible by either 17 or 23. - 11 is not divisible by either 17 or 23. - 19 is not divisible by either 17 or 23. - Therefore, X cannot be 9.

Based on the analysis above, the only possible value for X is 7.

Therefore, the first digit of the number is 7.

Note: The analysis above is based on the given conditions and the search snippets provided.