## Problem #002 - a bag full of numbers

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Two friends were bored and decided to play a game... a mathematical game with a paper bag!

### Problem statement

John and Mary have a bag full of integer numbers. In fact, the bag has $$10^{10^{10}}$$ integers, each written on a plastic card, and the sum of all the $$10^{10^{10}}$$ integers in the bag is $$0$$. In turns, Mary and John are going to play with the bag by doing the following:

• Picking two cards from the bag with numbers $$a$$ and $$b$$ and removing them from the bag;
• Inserting a new card in the bag with the number $$a^3 + b^3$$.

Is there any initial number configuration and/or set of moves for which it is possible that, after $$10^{10^{10}} - 1$$ moves, the only card in the bag has the number $$73$$?

### Solution

You can read the solution here to compare with your own solution.

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