How Many Dominoes to Knock Over a Skyscraper?

Estimate the Fewest Number of Dominoes Needed to Knock Over a Skyscraper-sized Domino.

Starting with a 1 cm domino, each subsequent one can knock over another domino 1.5 times its height. What is the fewest number of dominoes you need to knock over a domino as tall as a skyscraper?

Answer:

To knock over a skyscraper-sized domino starting with a 1 cm domino, each subsequent one being able to knock over another domino 1.5 times its height, we estimate it would require 30 dominoes.

Estimating the fewest number of dominoes needed to knock over a skyscraper-sized domino involves understanding geometric progression. In this scenario, each domino is able to topple over a domino 1.5 times its height, creating a sequence of increasing heights.

If we consider a skyscraper to be approximately 150 meters tall, we can calculate how many times we need to multiply the height of the initial 1 cm domino by 1.5 to reach or exceed this height. By following the progression of increasing heights, we find that it would take 30 dominoes, including the original 1 cm domino and the subsequent dominoes it knocks over, to reach the height of a skyscraper.

This example showcases how geometric progression can be utilized to estimate larger lengths based on the properties of smaller objects. By expanding our understanding of basic mathematical concepts, we can tackle complex estimation problems with confidence and creativity.