how many natural three digit numbers have the property that the difference between each two neighbor digits is 3?
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Answer:
The average is g where g=every number in the group added together divided by the amount of numbers in the group. We have 3 digit numbers and are excluding one of the digits. This means that the average will be x and z added and then divided by 2 where x=first number and z=last number. We know that the two numbers must be evenly divisible by 2 when added since we cannot have a fraction as the second digit. The answers are the following: 111, 123, 135, 147, 159, 210, 222, 234,246,258, 321, 333, 345, 357, 369, etc. As you can see, there are 5 numbers with each number single digit number as the first digit. So, with 3xy, the x’s and y’s could be one of 5 numbers each. So for every single digit number (other than 0), we will have five numbers. There are exactly 9 numbers we can use. This means that we will have 9 sets of 5. This is 9*5 or 45. There are 45 of them. However, if we include negative numbers, there are 90 of them. We do not include numbers starting with 0 as the 0 is only a placeholder and therefore does not count as a digit.
Step-by-step explanation:
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