Darwin's Drawer

This curious 3x3x3 drawer cabinet stores four puzzle pieces. The only complication is that the drawer has a high back and low front. As more pieces are being packed, the drawer quickly becomes restricted from opening, thus minimizing the prospect of fitting in new ones. To keep track of the inside's whereabouts, Darwin's Drawer has a convenient grid on top. Packing the drawer with the full set of four requires you to find a unique solution among almost a hundred-thousand possible assemblies. Only the fittest puzzlers will survive this test!