Problems
1. How many Legos is required to build a staircase with five levels? Six? Ten?
2. How could you determine the number of Legos needed for a staircase with 100 levels?
3. What is the highest staircase you could build with 10,000 Legos? How many Legos would you have remaining?
POW! #4: The Staircase Problem
Problem Statement
In the Problem of the Week: The Staircase Problem, I am going to find out how many Legos it takes to build a Lego staircase. In order to do this, I am going to create a formula. I am going to test my formula by using it to find the amount of Legos in a five level staircase, a six level staircase, a ten level staircase, and a one-hundred level staircase. Then I will find out how many levels can be built with ten-thousand Legos. The goal of this problem is to find a formula that will find the amount of Legos in a certain leveled staircase.
Process
In order to see the growth of Legos, first I drew 5 staircases with levels one to five on a sheet of graph paper. After drawing the staircases, I counted the number of squares on each leveled staircase and plotted it onto a XY Chart. Then I analyzed the chart. I noticed that as the staircase increases levels, the total number of Legos increases by the total number of Levels. The formula that I came up with is #Legos = #Levels (0.5 (#Levels) + 0.5) or #Legos = 0.5(#Levels 2 + #Levels). Next, I used my formula in order to solve for the number of legos in a five, six, and ten level staircase. The number of Legos in a five level staircase was 15, the number of Legos in a six level staircase is 21, and the number of Legos in a ten level staircase is 55. Next I tried my formula with 100 levels. After solving the equation, I got 5,050 Legos. The last challenge for me was to use my formula in order to find out how many Levels can be built with 10,000 Legos. In order for me to use my problem in order to find Levels instead of Legos, I plugged in 10,000 for Legos. Then I attempted to solve the problem. I was unable to find an accurate answer to the problem, so I used a calculator and increased the number of Levels until I got an answer close enough to 10,000 Legos, but not over. The closest number of Levels that I got was 140 Levels, which is equal to 9,870 Legos. Then I used the 9,870 Legos and subtracted from 10,000 in order to find the remainder.
Solution
In the end I found out that the amount of Legos in a five level staircase is 15, the number of Legos in a six level staircase is 21, and the number of Legos in a ten level staircase is 55. In an one-hundred level staircase, there are 5,050 Legos. Finally, you can build a 140 Level staircase with 10,000 Legos and have 130 Legos remaining.
Data
Problem Statement
In the Problem of the Week: The Staircase Problem, I am going to find out how many Legos it takes to build a Lego staircase. In order to do this, I am going to create a formula. I am going to test my formula by using it to find the amount of Legos in a five level staircase, a six level staircase, a ten level staircase, and a one-hundred level staircase. Then I will find out how many levels can be built with ten-thousand Legos. The goal of this problem is to find a formula that will find the amount of Legos in a certain leveled staircase.
Process
In order to see the growth of Legos, first I drew 5 staircases with levels one to five on a sheet of graph paper. After drawing the staircases, I counted the number of squares on each leveled staircase and plotted it onto a XY Chart. Then I analyzed the chart. I noticed that as the staircase increases levels, the total number of Legos increases by the total number of Levels. The formula that I came up with is #Legos = #Levels (0.5 (#Levels) + 0.5) or #Legos = 0.5(#Levels 2 + #Levels). Next, I used my formula in order to solve for the number of legos in a five, six, and ten level staircase. The number of Legos in a five level staircase was 15, the number of Legos in a six level staircase is 21, and the number of Legos in a ten level staircase is 55. Next I tried my formula with 100 levels. After solving the equation, I got 5,050 Legos. The last challenge for me was to use my formula in order to find out how many Levels can be built with 10,000 Legos. In order for me to use my problem in order to find Levels instead of Legos, I plugged in 10,000 for Legos. Then I attempted to solve the problem. I was unable to find an accurate answer to the problem, so I used a calculator and increased the number of Levels until I got an answer close enough to 10,000 Legos, but not over. The closest number of Levels that I got was 140 Levels, which is equal to 9,870 Legos. Then I used the 9,870 Legos and subtracted from 10,000 in order to find the remainder.
Solution
In the end I found out that the amount of Legos in a five level staircase is 15, the number of Legos in a six level staircase is 21, and the number of Legos in a ten level staircase is 55. In an one-hundred level staircase, there are 5,050 Legos. Finally, you can build a 140 Level staircase with 10,000 Legos and have 130 Legos remaining.
Data