Question

Используя цифры 4 5 6 записали два разных трехзначных числа. Может ли произведение них чисел быть равным числу записанных только с помощью цифр 0 2 3 5 6 8? (В записи чисел цифры не повторяются)

Answer 1

Всего какие могут быть варианты
       456 465   546     564 645 654
456  -      -          -            -      -        -       
465  -      -   253980       -      -       -
546  -    253980 -         -       -        -
564  -     -          -         -         -      -
645  -     -         -        -         -    - 
654  -    -         -       -        -      -                         у меня не получилось найти такого числа . Максимально приближеное к нужному получилось при умножении 465 546 но 9 не 6 поэтому не подходит, остальные слишком различаются 

Answer 2

Solving the Problem

To solve this problem, we need to find two different three-digit numbers using the digits 4, 5, and 6. Then, we'll check if the product of these two numbers can be represented using only the digits 0, 2, 3, 5, 6, and 8.

Let's start by finding the two different three-digit numbers using the digits 4, 5, and 6.

Finding Three-Digit Numbers

The possible combinations of the digits 4, 5, and 6 for forming three-digit numbers are: - 456 - 465 - 546 - 564 - 645 - 654

Now, let's check if the product of any two of these numbers can be represented using only the digits 0, 2, 3, 5, 6, and 8.

Checking the Product

Let's calculate the products of these pairs and see if any of them can be represented using the specified digits.

1. Product of 456 and 465: - 456 * 465 = 211,560 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

2. Product of 456 and 546: - 456 * 546 = 248,976 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

3. Product of 456 and 564: - 456 * 564 = 257,184 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

4. Product of 456 and 645: - 456 * 645 = 293,520 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

5. Product of 456 and 654: - 456 * 654 = 298,224 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

6. Product of 465 and 546: - 465 * 546 = 253,890 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

7. Product of 465 and 564: - 465 * 564 = 262,260 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

8. Product of 465 and 645: - 465 * 645 = 300,225 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

9. Product of 465 and 654: - 465 * 654 = 304,710 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

10. Product of 546 and 564: - 546 * 564 = 307,584 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

11. Product of 546 and 645: - 546 * 645 = 351,570 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

12. Product of 546 and 654: - 546 * 654 = 356,724 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

13. Product of 564 and 645: - 564 * 645 = 363,780 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

14. Product of 564 and 654: - 564 * 654 = 369,336 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

15. Product of 645 and 654: - 645 * 654 = 421,830 - This product cannot be represented using only the digits 0, 2, 3, 5, 6, and 8.

Conclusion

After checking all the possible products of the given three-digit