Task B-1.4. The number 123456789 is given. How many and which digits need to be deleted so that the new number is divisible by 36?
Solution. For the given number to be divisible by 4, it must be even, and its two-digit ending must be divisible by four. Therefore, we must delete the last digit 9 and the digit 7. Then the number ends with 68, which is divisible by 4.

(2 points)

The required number must also be divisible by 9, which means the sum of its digits must be divisible by 9. Since the current sum of the digits is 29, it only remains to delete the digit 2 to get 27, which is divisible by 9.

And that is the only such possibility because the next number divisible by 9 is 18, which cannot be obtained by deleting only one digit.

(2 points)