100% Natural!

Probability Level 5

All the natural numbers from 1 to 100 are arranged in a circle such that each number is either larger than both of its neighbours, or smaller than both of its neighbours. A pair of neighbouring numbers is good if the above-described property holds. What is the minimum number of pairs that can be good ?


The answer is 51.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Harish Ghunawat
Jun 7, 2015

let the no. be arranged normally from 1 to 100 then pairs will be 50 and one more pair will be (1,100) since they are in circle so total pair would be 51

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I thought it should be 100 pairs since they are placed in a circle, such as:1-2,2-3,3-4,4-5,etc. Besides, the problem asks for the minimum, not the maximum. I'm not claiming I'm right: my answer is stated to be wrong, but I couldn't see why.

Ngoc Nguyen - 5 years, 12 months ago

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