Anna picked 6 cards from these 10 digit cards to form a 6-digit number: 0 1 2 3 4 5 6 7 8 9, then asked Ola to guess what number she made. 1.Only the first digit is an odd number.2.The digit in the ten thousands place is twice the digit in the ones place.3.The number is 800 000 when rounded to the nearest 100 000.4.The number is the same if you round it to the nearest 10 000 and to the nearest 1000. The odd dogits are: 1 3 5 7 9. What is the number?

780264

780624

780264

To find the number that Anna made, let's analyze the given information step by step.

1. Only the first digit is an odd number.
Since we know that the first digit is an odd number, it means it can only be one of these: 1, 3, 5, 7, or 9.

2. The digit in the ten thousands place is twice the digit in the ones place.
Since the number is a 6-digit number, the digit in the ten thousands place is the first digit. And according to the first condition, it is an odd number. The only odd number in our available digits is 1. Also, it is mentioned that the tens thousands place is twice the digit in the ones place. So, the number in the ones place must be half of 1, which is 0 (since we only have digits available from 0 to 9).

So far, we know that the number starts with 10.

3. The number is 800,000 when rounded to the nearest 100,000.
This condition narrows down our possibilities. The rounded number means the last digit of the original number will be either 5 or 0. But since we already used the digit 0 for the ones place, the only possibility is the last digit being 5.

The number now has the form 10X00X5.

4. The number is the same if you round it to the nearest 10,000 and to the nearest 1,000.
This means that the digit in the hundreds place and the thousands place must be the same. But since we have already used the digit 0 in the ones place, we need to find the digit that is still available from the remaining odd digits: 1, 3, 7, or 9. The only digit that fulfills this condition is 1.

The number can now be represented as 1010X15.

Combining all the conditions, the number Anna made is 101015.