POW 4: The Staircase Problem
1. Problem Statement
For this problem, we are trying to determine how many Lego blocks it would take to build a staircase of any height. The diagram in the pictures shows a 4-level staircase. It is made of 10 blocks. The bottom level has 4, the second has 3, the third level has 2 and the top level has one.
Process:
So for the process of solving the problem, the staircase is made of blocks, one stair is 1, second is 2, third is 3, and the fourth is 4. For this problem we are given an equation: n(n+1)/2, so in a way you're writing this out in a "T" chart for x and y. When writing your numbers under x you write it out as 1, 2, 3, 4. For y, 1, 3, 6, 10. Now to make it sound simple, an easy way you can do this problem is you can stack the stair case on top of each other, and it would make a perfect square. Why would you do this you may ask? Well lets use our equation n(n+1)/2, you can plug in the numbers for x and y. So lets use 2 as an example. 2(2+1)/2. So we would start with the parentheses: (n+1), if we plug in 2 for n it would look like (2+1), that would equal 3. So now the problem would turn into 2(3)/2, 2*3 is 6, divide by 2 and you get 3, which is your y on the "T" chart. I did the same process to get my answer, and what I got for my final answer was 5,050,000. The correct answer was 50,050,000. If I just moved the decimal over by 1 I would have gotten the correct answer.
For this problem, we are trying to determine how many Lego blocks it would take to build a staircase of any height. The diagram in the pictures shows a 4-level staircase. It is made of 10 blocks. The bottom level has 4, the second has 3, the third level has 2 and the top level has one.
Process:
So for the process of solving the problem, the staircase is made of blocks, one stair is 1, second is 2, third is 3, and the fourth is 4. For this problem we are given an equation: n(n+1)/2, so in a way you're writing this out in a "T" chart for x and y. When writing your numbers under x you write it out as 1, 2, 3, 4. For y, 1, 3, 6, 10. Now to make it sound simple, an easy way you can do this problem is you can stack the stair case on top of each other, and it would make a perfect square. Why would you do this you may ask? Well lets use our equation n(n+1)/2, you can plug in the numbers for x and y. So lets use 2 as an example. 2(2+1)/2. So we would start with the parentheses: (n+1), if we plug in 2 for n it would look like (2+1), that would equal 3. So now the problem would turn into 2(3)/2, 2*3 is 6, divide by 2 and you get 3, which is your y on the "T" chart. I did the same process to get my answer, and what I got for my final answer was 5,050,000. The correct answer was 50,050,000. If I just moved the decimal over by 1 I would have gotten the correct answer.