a three-digit number satisfies these condition: thedigits are consecutive whole numbers; the sum of the digits is greater than 10 and less than 20; and the tens digit is an odd number. what is the number
456 , if consecutive from left to right
654 if consecutive from right to left
To find the three-digit number that satisfies the given conditions, we can break down the problem into steps:
Step 1: Identify the possible range for the tens digit.
Since the tens digit must be an odd number, we consider the set of odd numbers between 1 and 9, inclusive. These numbers are: 1, 3, 5, 7, and 9.
Step 2: Find the possible values for the units digit.
The units digit can only be consecutive to the tens digit, so we consider each odd number from Step 1 as the tens digit, and find the two consecutive numbers that follow it. These pairs of numbers will be the possible units digits for each tens digit:
For 1: 2, 3
For 3: 4, 5
For 5: 6, 7
For 7: 8, 9
For 9: no consecutive odd numbers follow.
Step 3: Calculate the sum of the digits for each three-digit number.
For each tens and units digit combination from Step 2, calculate the sum of the digits.
For 123, the sum of the digits is 1 + 2 + 3 = 6.
For 134, the sum of the digits is 1 + 3 + 4 = 8.
For 456, the sum of the digits is 4 + 5 + 6 = 15.
For 578, the sum of the digits is 5 + 7 + 8 = 20.
Step 4: Identify the three-digit number that satisfies the conditions.
From the calculations in Step 3, we can see that the sum of the digits must be greater than 10 and less than 20. Therefore, the only three-digit number that satisfies all the conditions is 456.
So, the three-digit number that satisfies the given conditions is 456.