Be Not Greedy (Problem #1)
You have some number of candies you want to divide among three people. It's possible to evenly divide the candies among three. But you want to give each person a different number of candies (leaving the most for yourself) such that no two of the three can evenly divide their candies between themselves.
Can you do this?
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1 solution
No you cannot. If person 1 receives an odd number of candies and person 2 receives an even number of candies, person 3 (if he receives an odd number of candies) will be able to divide the candy with person 1 and (if person 3 receives an even number of candies) will be able to evenly divide the candy with person 2. Person 1 and person 2 cannot split the candies between them.