Equal numbers in a circle

Source: Stanford Math Circle Sunday May 30, 2010

Problem: A circle is divided into 6 sectors. The numbers 1, 0, 1, 0, 0, 0 are written into the sectors in the counter clock-wise direction. You may increase any two neighboring numbers by 1. Is it possible to make all of the numbers equal?

Disclaimer: Think simple. Very simple problem. Solved it in less than 30 seconds. :)

Solution: Posted by Aman in comments!! He claims he took less than 10 seconds \m/ \m/. This is one thing where it feels good to win, but feels awesome to be defeated \m/ \m/


  1. Simple problem, Me solved it in less than 10 seconds \m/
    Add all the numbers in odd places and subtract from this sum, the sum of the number at even places. The result is invariant and is = 2. The final state would demand a result = 0 and hence is not possible.:)

  2. Great.. Nice and simple solution.. Thanks.. :)

  3. Damn it!
    @ Aman : Awesome solution. It was very difficult to think this simple!

  4. ~2 mins before I read your comment on time to be taken :P
    Got it :) in 30 sec. thereafter


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