What is the maximum number of rectangular blocks, each with dimensions $$12$$ centimeters by $$6$$ centimeters by $$4$$

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What is the maximum number of rectangular blocks, each with dimensions $$12$$ centimeters by $$6$$ centimeters by $$4$$

by M7MBA » Sun Sep 19, 2021 12:43 am

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What is the maximum number of rectangular blocks, each with dimensions $$12$$ centimeters by $$6$$ centimeters by $$4$$ centimeters, that will fit inside a rectangular box $$X?$$

(1) When box $$X$$ is filled with the blocks and rests on a certain side, there are $$25$$ blocks in the bottom layer.
(2) The inside dimensions of box $$X$$ are $$60$$ centimeters by $$30$$ centimeters by $$20$$ centimeters.