What is Jared's favorite six-digit number if the ten digit is his favorite digit, the sum of the hundred thousand digit and the thousand digit in his number from the largest place value to the smallest place value are consecutive numbers?
It’s 123456
To find Jared's favorite six-digit number, we need to determine the specific values of each digit based on the given information. Let's break down the problem step by step:
Step 1: The favorite digit is the ten-thousands digit.
Step 2: The sum of the hundred-thousands digit and the thousands digit is equal to consecutive numbers.
Based on these steps, we can start solving the problem.
Step 1: The favorite digit is the ten-thousands digit.
Knowing this, we can represent Jared's six-digit number as follows:
ABCTDE
The digit B represents Jared's favorite digit.
Step 2: The sum of the hundred-thousands digit and the thousands digit is equal to consecutive numbers.
Based on this information, we know that either:
A + C = B - 1, where A is the hundred-thousands digit and C is the thousands digit.
Or
A + C = B + 1, where A is the hundred-thousands digit and C is the thousands digit.
To continue, we need more specific information about Jared's favorite digit or any constraints regarding the range of values for each digit.
To find Jared's favorite six-digit number, we need to follow the given conditions. Let's break down the problem step by step:
1. The ten's digit is Jared's favorite digit: This means the ten's digit can be any number from 0 to 9.
2. The sum of the hundred thousand digit and the thousand digit is consecutive: The hundred thousand digit and the thousand digit have consecutive values. Consecutive numbers are those that follow each other in order without any gaps. For example, 2 and 3, 5 and 6, etc.
Now, let's try to narrow down our options by considering the second condition. Since we are looking for a six-digit number, the hundred thousand digit and the thousand digit must be consecutive numbers from the largest place value to the smallest. Let's consider the possibilities:
Option 1: The hundred thousand digit is 9 and the thousand digit is 8. In this case, we have _ 9 _ 8 _ _. The remaining digits can be any numbers from 0 to 9.
Option 2: The hundred thousand digit is 8 and the thousand digit is 7. In this case, we have _ 8 _ 7 _ _. The remaining digits can be any numbers from 0 to 9.
Option 3: The hundred thousand digit is 7 and the thousand digit is 6. In this case, we have _ 7 _ 6 _ _. The remaining digits can be any numbers from 0 to 9.
Option 4: The hundred thousand digit is 6 and the thousand digit is 5. In this case, we have _ 6 _ 5 _ _. The remaining digits can be any numbers from 0 to 9.
Option 5: The hundred thousand digit is 5 and the thousand digit is 4. In this case, we have _ 5 _ 4 _ _. The remaining digits can be any numbers from 0 to 9.
Option 6: The hundred thousand digit is 4 and the thousand digit is 3. In this case, we have _ 4 _ 3 _ _. The remaining digits can be any numbers from 0 to 9.
Option 7: The hundred thousand digit is 3 and the thousand digit is 2. In this case, we have _ 3 _ 2 _ _. The remaining digits can be any numbers from 0 to 9.
Option 8: The hundred thousand digit is 2 and the thousand digit is 1. In this case, we have _ 2 _ 1 _ _. The remaining digits can be any numbers from 0 to 9.
Option 9: The hundred thousand digit is 1 and the thousand digit is 0. In this case, we have _ 1 _ 0 _ _. The remaining digits can be any numbers from 0 to 9.
With these options in mind, we have a total of 10 possibilities for the ten's digit and 9 possibilities for each of the other remaining digits.
To determine Jared's favorite six-digit number, we need additional information to narrow down the choices. Can you provide any additional conditions or restrictions?
We have six digits and we know that ten digit is his favorite and also that (hundred thousand digit + thousand digit) is also his favorite number, so:
2 3 4 5 6 7 would work because
2(100,000 digit)+ 4(thousand digit)=6
and we know that this sum is his favorite number;
and
6(10 digit) is also his favorite number,
and the numbers written above are in consecutive order, so his favorite six digit number is 234,567.
Please feel free to correct me!