<ul><li>Soldiers tasked with stacking cannonballs must arrange them in tetrahedra as per the new commander's OCD requirements.</li><li>The number of cannonballs in the nth tetrahedron layer is known as the nth tetrahedral number.</li><li>Not every number is a tetrahedral number, but it's usually possible to stack any number into no more than four tetrahedra.</li><li>Two ways to meet the commander's demands are listed: avoiding certain numbers or allowing negative cannonballs for stacking.</li><li>Sir Frederick Pollock's conjecture on tetrahedral numbers, proposing sums of at most five tetrahedral numbers, is still open.</li><li>Negative cannonballs can be used to stack any integer as the sum of four tetrahedral numbers.</li><li>A Python code check function is provided to determine if an arrangement of n cannonballs into four tetrahedral piles is possible.</li><li>The use of formulas to generalize definitions, like in tetrahedral numbers, requires conscious handling for better understanding.</li></ul>

Stacking positive and negative cannonballs

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