Friendly neighbors

Probability Level 4

I have a list of twelve numbers where the first number is 1, the last number is 12 and each of the other numbers is one more than the average of its two neighbors. What is the largest number in the list?


The answer is 37.

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Victor Loh by Victor Loh , 19, Singapore

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1 solution

Ajit Athle
Aug 1, 2014

Assume the series to be 1, (3+x)/2, x and so on whence you'll get the 12th term as (11x-207)/2 which is 12 giving x=21 and thus the series is: 1, 12, 21, 28, 33, 36, 37, 36, 33 28, 21 & 12.

5 Helpful 0 Interesting 1 Brilliant 2 Confused

According to your question, you have a list of numbers with 1 as 1st and 12 as 12th and the OTHER numbers are an average of their two neighbors. So how do u explain your equation for the 12th number.. There is no 13th number with whom the average of the 11th is the 12th number.

Chinmay Raut - 6 years, 9 months ago

I do not understand how to show where x came from or that first equation.

Omid Hussaini - 1 month ago

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