Create an odd number that satisfy the following clues
_ Thousand digit is twice ones digit
_ Ten thousand digit is three times the tens digit
_ Each digit is used only once
Thousand digit is twice ones digit: ones digit must be odd
2xx1 , 6xx3 , no others possible
Ten thousand digit is three times the tens digit
2xx1 -----> 92x31, for tens digit, can't use 1,2,4, ..., each digit used only once
6xx3 ---> none possible
92x31 -----> the remaining x could be 0,4,5,7,8,9 ,
e.g. 92731 follows all the given restrictions
How many will there be ?
Can you list them for me?
Did I miss any?
Thdghb
Sure, here's an odd number that satisfies the clues:
43,265
To create an odd number that satisfies the given clues, let's go through the steps:
Step 1: Start by listing the digits 0 to 9.
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Step 2: Let's consider the thousands, hundreds, tens, and ones digits.
_ Thousands digit is twice ones digit.
_ Ten thousands digit is three times the tens digit.
_ Each digit is used only once.
Step 3: Determine the restrictions on each digit based on the clues.
Since the number is odd, the ones digit must be an odd number. Therefore, it must be either 1, 3, 5, 7, or 9.
The thousands digit is twice the ones digit, so it must be even. Based on the digits available, the only options for the thousands digit are 2, 4, 6, or 8.
The ten thousands digit is three times the tens digit, which means it must be divisible by 3. But since we have already used the digit 9 for the ones place, it cannot be the ten thousands digit. Therefore, the ten thousands digit can only be 3 or 6.
The remaining digits available for the hundreds digit are 0, 4, 5, and 7.
Step 4: Combine the digits to create the number.
Let's try different combinations to satisfy the clues and create an odd number:
Option 1:
Ten thousands digit: 3 (three times the tens digit)
Thousands digit: 6 (twice ones digit)
Hundreds digit: 0
Tens digit: 1
Ones digit: 5
The number formed: 30615
Option 2:
Ten thousands digit: 3 (three times the tens digit)
Thousands digit: 6 (twice ones digit)
Hundreds digit: 4
Tens digit: 0
Ones digit: 7
The number formed: 36407
So, two possible odd numbers that satisfy the given clues are 30615 and 36407.
To create an odd number that satisfies the given clues, we need to consider the possible digit combinations.
Let's start by solving the first clue: The thousand digit is twice the ones digit.
An odd number cannot end with an even digit. Therefore, the ones digit has to be an odd number. The only possible odd digits are 1, 3, 5, 7, and 9.
Since the thousand digit is twice the ones digit, it has to be an even number. It can be 2, 4, 6, or 8. Since we need to use each digit only once, let's try with digit 2 as the thousand digit.
Now, let's move to the next clue: The ten thousand digit is three times the tens digit.
To make an odd number, the tens digit should be an odd number, which can be either 1, 3, 5, 7, or 9.
The ten thousand digit should be three times the tens digit. Therefore, let's consider the options:
1. If the tens digit is 1, then the ten thousand digit would be 3. However, we have already used digit 3.
2. If the tens digit is 3, then the ten thousand digit would be 9. However, we have already used digit 9.
3. If the tens digit is 5, then the ten thousand digit would be 1, but we have already used digit 1.
4. The other remaining options (7 and 9) are not divisible by 3, so they would not satisfy the clue.
Therefore, it is not possible to find a number that satisfies all the given clues with the conditions provided.