10. I am a number between 7 000 000 and 8 000 000.
All my digits are odd.
All the digits in my thousands period are the same.
All the digits in my units period are the same.
The sum of my digits is 31.
What number am l?
Give as many answers as you can.
What strategies did you use to find the
mystery number?
7,555,333
7,333,555
7,111,777
7,777,111
hte4rgc44444rrrrrrrr
6000000000
To find the mystery number, we can use a step-by-step approach and some logical reasoning:
1. The number is between 7,000,000 and 8,000,000, so it must start with a 7.
2. All the digits are odd, which means they can only be 1, 3, 5, 7, or 9.
3. The sum of the digits is 31, so when trying different combinations, make sure the sum of the digits is always 31.
4. The thousands period has all the same digits. Since the sum of the digits is 31 and they are all odd, this means there must be an odd number of digits in the thousands period.
Now, let's try finding the mystery number using these strategies:
- Starting with the thousands period, we have an odd number of digits, so it could be 111, 333, 555, 777, or 999.
- Next, let's try finding the units period. Since the sum of the digits is 31, and they are all odd, we can make combinations such as 1, 3, 5, and 9 that add up to 31. For example, 3+5+5+9+9 would be a valid combination. Therefore, the units period options could include numbers like 33559, 59555, 333331, etc.
Now, let's combine the thousands period and the units period options we discovered:
- If we combine 111 as the thousands period with 33559 as the units period, we get the number 7,033,559.
- If we combine 111 as the thousands period with 59555 as the units period, we get the number 7,059,555.
- If we combine 333 as the thousands period with 333331 as the units period, we get the number 7,333,331.
These are a few examples of possible answers based on the given information.