Stacking Lego to the Sky

Lego, those colorful, clicking, bumpy toy bricks, lets you make just about anything you can think up. And if you have enough bricks, you can really go big. So our friends Mikey and Mateo C. asked, how many would it take to reach the top of the Empire State Building? Well, to start we need to know its height. For a long time it was the tallest building in the world, from 1931 until the first World Trade Center went up in 1970. Now we have to decide whether to count just the building itself, which is 1,250 feet, or to the top of its antenna, which stands 1,454 feet high. Let’s go with the whole shebang for fun. Lego bricks are 9.6 millimeters thick, just shy of 1 centimeter (a bit less than 1/2 inch). So 1,000 Legos are 9.6 meters tall, or 31 1/2 feet – and that’s only 2 or 3 floors! Let’s find out how much Lego we need to build to the sky.

Wee ones: If you stack red, green, blue, yellow, and white Lego pieces, how many colors is that?

Little kids: If you’re stacking a 10-brick chunk and you have 8 bricks so far, how many more bricks do you need?  Bonus: If you speed things up by stacking 100-brick chunks up to 900 bricks, what numbers do you say to count up by 100s?

Big kids: If you have 9 blue bricks, and your stacking pattern is red, blue, yellow, blue, blue, do you have enough blues to keep up that pattern for 15 bricks?  Bonus: If we round off and say 1,000 Legos stack 30 feet tall, and the Empire State Building stands about 1,500 feet tall, how many bricks do we need to stack — and will our guess be over or under the real number?

Answers:
Wee ones: 5 colors.

Little kids: 2 more bricks.  Bonus: 100, 200, 300, 400, 500, 600, 700, 800, 900.

Big kids: Yes! You need 3 sets of that 5-brick pattern, each of which has 3 blues, and 3 x 3 = 9.  Bonus: 50,000 Legos, since you’ll need 50 sets of 30 feet, and there are 1,000 Legos per set. But 1,000 Legos stand taller than that, so you’d need fewer sets — plus the building is shorter than 1,500. So our guess is over the real number, 46,165 bricks (rounding up from 46,164 1/2).

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