What are the two consecutive numbers that have digit sums of 36 and 1
9,999 and 10,000
Let's solve this step-by-step.
Step 1: Find the two consecutive numbers.
Let's assume the first number is N. Since we are looking for consecutive numbers, the next number is (N+1).
Step 2: Calculate the digit sum of N.
To find the digit sum of a number, add up all its digits. In this case, we know the digit sum of N is 36.
Step 3: Find the digit sum of (N+1).
Similarly, we need to find the digit sum of (N+1), which is 1.
Step 4: Set up the equation.
The digit sum of a number can be found by summing its digits. So, for N, we write the equation:
N = sum of digits
Similarly, for (N+1) we can write:
(N+1) = sum of digits
Step 5: Solve the equation.
Since the digit sum of N is 36, we can write:
N = 36
And since the digit sum of (N+1) is 1, we can write:
(N+1) = 1
Step 6: Solve for N.
From the equation (N+1) = 1, we can subtract 1 from both sides:
N = 0
So, the first number is 0.
Step 7: Find the consecutive number.
Since the next number is (N+1), we have:
(N+1) = (0+1) = 1
Therefore, the consecutive numbers with digit sums of 36 and 1 are 0 and 1, respectively.
To summarize:
First number: 0
Second number: 1
To find the two consecutive numbers with digit sums of 36 and 1, we need to understand what the digit sum is. The digit sum of a number is the sum of its individual digits. For example, the digit sum of 36 would be 3 + 6 = 9.
First, let's consider the number with a digit sum of 36. Since the digit sum is 36, the number must consist of two digits that add up to 36. However, the highest sum we can get with two digits is 18 (9 + 9).
Therefore, it is not possible to find a two-digit number with a digit sum of 36. We need to consider larger numbers. Let's look at three-digit numbers.
If the digit sum is 36, the largest possible single digit we can have is 9. So, let's try to find a three-digit number where one of the digits is 9 and the other two digits add up to 27 (36 - 9).
By trying different combinations, we find that 189 is the only three-digit number that satisfies these conditions. The digit sum of 189 is 1 + 8 + 9 = 18.
Now, let's find the next consecutive number. We add 1 to 189, and we get 190. The digit sum of 190 is 1 + 9 + 0 = 10.
Therefore, the two consecutive numbers that have digit sums of 36 and 1 are 189 and 190.