Question

using python

Blocks in pyramid def pyramid_blocks (n, m, h) A pyramid structure (although more in the ancient Mesoamerican than the more famous ancient Egyptian style) is built from layers, each layer consistinga rectangle of identical cubic blocks. The top layer of the pyramid consists of n rows and m columns of such blocks. The layer immediately below each layer contains one more row and one more column, all the way to the bottom layer of the pyramid. If the entire pyramid consists of h such layers, how many blocks does this pyramid contain in total? Here you can solve this problem in a straightforward fashion by simply looping through the h layers and adding up all the blocks along the way in each layer. However, if you happen to know some discrete math and combinatorics, you can come up with an analytical closed form formula for the result and compute the answers much faster that way. (There is an important idea in that for us to think about in general.) Expected result h n 2 1 6 2 18 570 3212 10 11 12 100 100 2318350 100 E

Answer 1

Here is the completed code for this problem. Comments are included, go through it, learn how things work and let me know if you have any doubts or if you need anything to change. If you are satisfied with the solution, please rate the answer. Thanks

#code

#required method
def pyramid_blocks(n,m,h):
    #declaring number of blocks
    blocks=0
    #I dont have much knowledge in descrete math or combinatorics, so I'm doing
    #this the old fashioned way. the formula for finding number of blocks
    #is nm + (n+1)(m+1) + (n+2)(m+2) + ... + (n+h-1)(m+h-1)
    #looping from i=0 to i=h-1
    for i in range(h):
        #finding (n+i * m+i) and adding to blocks
        blocks+=(n+i)*(m+i)
    #returning blocks
    return blocks


#testing
print(pyramid_blocks(2,3,1))
print(pyramid_blocks(2,3,10))
print(pyramid_blocks(10,11,12))
print(pyramid_blocks(100,100,100))

#output

6

570

3212

2318350