Quandaries and Queries


     My name is Hernan and I am trouble solving the following problem: Can one place 15 integers around a circle so that the sum of every 4 consecutive numbers is equal either to 1 or 3?. Please help me because I have no idea how to do it. Many thanks


Hi Hernan,

One way to approach it is to ask yourself: If, after successfully placing 15 integers as prescribed, you were to add up all the fifteen sums of four consecutive numbers, would you get an odd or an even result?

Perhaps you can make a diagram representing the quantities to add up to help you come up with two conflicting answers.



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