A warehouse has a bunch of 1 foot x 1 foot x 1 foot crates, stacked to
form a bigger cube that is 10 feet x 10 feet x 10 feet. After receiving
a large order, the warehouse foreman called the stockboy into his office,
gave him 1000 labels and told him to label all of the crates for shipment.
Being the lazy person he was, the stockboy only labeled the crates showing, and threw the rest of the labels away.
How many labels did he throw away?
Scroll down for the answer.
The Answer:
Assuming he only put one label on each box, he threw away 576 labels.
There are 2 ways to solve this problem:
1. The red block in the middle represents a block of 8 deep x 8 wide x 9 high crates (576 crates) the stockboy can't get to, because they are covered by other crates, so he won't label them.
2. The green are blocks of 1 deep x 8 wide x 10 high (80) crates, the blue is a block of 8 deep x 8 wide x 1 high (64) crates, and the yellow are blocks of 10 deep x 10 high x 1 wide (100) crates.
1000 crates total (10 x 10 x 10 = 1000) minus 424 that he can reach and label (100 + 100 + 80 + 80 + 64 = 424), leaves 576 extra lables he threw away.
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