Monday, 28 August 2017

3 digit numbers whose one digit is the average of the other two


Question: How many three-digit numbers are composed of three distinct digits such that one digit is the average of the other two?





How can this be solved with an arithmetic sequence?



I can see that any two digits must be same parity to produce the even sum. Also any two of the digits must be divisible by 2. if ¯abc is the digit, a+b=2c and doing that for all three digits gives three equations. Thats as far as I can get.

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