solutions to the problem what four-digit whole number satisfies the following conditons? The sum of the digits is 6; the number is less than 1200; none of the four digits are equal; and the tens digit is an odd number.
Since the sum of all 4 digits is only 6, and all digits are different, the smallest combination of digits that can be used is
1, 2, 3, 4
but that sum is already 10
There can be no such number.
however, using 0,1,2,3 the sum is 6
tens is odd
1032
Well, let's get down to the math circus! 🎪 To find the four-digit whole number that satisfies these conditions, we need to follow a step-by-step process.
First, let's focus on the sum of the digits, which is 6. We want to break down this number in a funny way. How about we imagine the number is a group of clowns with different weights? We need to distribute these weights, or digits, among our clowns.
Since we're aiming for a sum of 6, let's give the heaviest clown, which will be our thousands digit, a weight of 4. We still have 2 remaining to distribute among the other clowns.
Next, we want the tens digit to be odd. Unfortunately, odd clowns don't always play well with everyone, so we'll be a bit limited in our options. Our options for odd tens digits are 1, 3, 5, 7, or 9.
Since we've given 4 to the thousands digit, we have 2 left to divide between the hundreds and units digits. To ensure that none of the digits are equal, we need to make sure the hundreds and units digits are different. We'll start by giving the hundreds digit a weight of 2, leaving us with 0 for the units digit.
Putting it all together, the four-digit whole number that satisfies all the given conditions is 4210. Ta-da! 🎉
So, our clown show has the following weights: 4, 2, 1, and 0, which adds up to 6. But let's not keep them out of their circus caravan for too long; they have other clown duties to attend to!
To find a four-digit whole number that satisfies the given conditions, you can follow these steps:
Step 1: Determine all the possible values for the thousands digit:
Since the number should be less than 1200, the thousands digit can only be either 1 or 2.
Step 2: Determine all the possible values for the hundreds digit:
Since the sum of the digits is 6, the hundreds digit can be any integer from 0 to 6, excluding the value used for the thousands digit.
Step 3: Determine all the possible values for the tens digit:
Since the tens digit must be odd, you can choose from the set {1, 3, 5}.
Step 4: Determine all the possible values for the units digit:
The units digit will be the remaining value after considering the thousands, hundreds, and tens digits.
Step 5: Combine all the possible values to form four-digit whole numbers:
Based on the possible values determined from steps 1-4, you can combine them to form the following four-digit numbers:
1342, 1423, 1524, 2134, 2413, 2431, 3142, 3412, 4123, 4132, 4213, 4312
These are the various four-digit whole numbers that satisfy the given conditions, which are: the sum of the digits is 6; the number is less than 1200; none of the four digits are equal; and the tens digit is an odd number.
To find the four-digit whole number that satisfies the given conditions, we can break down the problem into smaller steps:
Step 1: Determine the possible values for the thousands digit.
Since the number is less than 1200, the thousands digit can only be 1 or 0.
Step 2: Determine the possible values for the hundreds digit.
The sum of the digits is 6, so the thousands digit and the tens digit must sum to 6. Since the thousands digit is either 1 or 0, the tens digit must be either 5 or 6. It should also be noted that the tens digit must be an odd number. So the possible values for the tens digit are 5 or 9.
Step 3: Determine the possible values for the tens digit.
Since all the digits must be unique, and we have already used the thousands and the tens digits, there are four digits remaining for the ones digit: 2, 3, 4, and 7.
Step 4: Combine all the possible values to find the four-digit whole number that satisfies the given conditions.
Combining the possibilities from steps 1, 2, and 3, we can find the following numbers that fulfill all the conditions:
1052, 1072, 1063, 1093, 1152, 1172, 1163, and 1193.
So, the four-digit whole numbers that satisfy the given conditions are: 1052, 1072, 1063, 1093, 1152, 1172, 1163, and 1193.