find the mystery number, it is a 4 digit odd number, all the digits are different, none of the digits are 0-9, the tens digit is twice the ones digit, and the hundreds digit is twice th tens digit. the thousands digit is one less than the hundreds digit?
I think the answer is 3,421
none of the digits are 0-9 ???
This doesn't make any sense.
To find the mystery number, let's break down all the given clues step by step:
1. The number is a 4-digit odd number: This means that the ones digit must be one of the odd digits 1, 3, 5, 7, or 9.
2. All the digits are different: Since each digit must be different from one another, we need to choose four different digits.
3. None of the digits are 0-9: This means that we cannot use any of the digits from 0 to 9.
4. The tens digit is twice the ones digit: From this clue, we can infer that the tens digit must be twice one of the odd digits chosen for the ones place. We can try all possible combinations: 2 * 1, 2 * 3, 2 * 5, 2 * 7, and 2 * 9.
5. The hundreds digit is twice the tens digit: Similar to the previous clue, the hundreds digit must be twice one of the even digits chosen for the tens place. We can try all possible combinations: 2 * 2, 2 * 4, 2 * 6, 2 * 8.
6. The thousands digit is one less than the hundreds digit: This clue tells us that the thousands digit is smaller than the hundreds digit by one. We can use the results from the previous clues to determine the possible values for the thousands digit.
Let's evaluate all the clues together:
Using the clues from step 4, we found that the ones digit (N) is 1, 3, 5, 7, or 9.
Using the clues from step 5, we found that the tens digit (T) can be 2, 4, 6, or 8.
Using the clues from step 6, we found that the hundreds digit (H) is one greater than the tens digit (T).
By using these clues, we can narrow down the possibilities:
If the tens digit (T) is 2, then the hundreds digit (H) is 3 (since 2 * 2 = 4 and 3 * 2 = 6).
Lastly, since the thousands digit is one less than the hundreds digit, then the thousands digit (M) must be 2 (since 3 - 1 = 2).
So, based on the given conditions, the mystery number can be 2361.