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Were talking about a problem involving putting numbers into boxes and other shapes. And the shape is an arrangement of boxes that looks something like this. And Ive got a certain number of boxes in the first row, so I have four boxes in the first row, and two in the second row, and one in the third row. And the rule is that these numbers must be decreasing. And the second rule is that the boxes are left-justified. And thats it! Thats the rule. A simple example would be this, heres a square. Three boxes in the first row, three in the second row, and three in the third row. The number of boxes in two rows can be the same. Another example of a shape would be something like this. This is something we call a staircase. Four, and three, and two, and one. Another shape thats kind of interesting, it turns out, for my purposes, is where I have two rows of the same length. This would be the shape (6,6). Why dont we put numbers in them? And so maybe I can even do it with these shapes and
