Building your own Mt. of Dew
Since this is a challenge, it's expected that you will want to make your own. This is meant to help you.
If you're going to make a pyramid, I did a little calculation for you. As your numbers grow, and it's time to make a pyramid, you'll
need to decide what kind to make. How many sides works well for the number of cans you have? How many cans are in the base of the
Mountain? How tall will it be? How wide is the base?
I calculated the base sizes, number of levels, height, and total number of cans needed
for bases of 3, 4 or 6 sides.
I did 3, 4 and 6 sides because thoses are the easiest numbers to do if you want to make a 7 sided pyramid, go ahead but don't ask me.
I do reserve the right to be wrong on the calculations.
Ryan Krueger
RSKrueger@taylorcorp.com
3 sided 
#total  #base  #level  height 
1  1  1  0.38' 
4  3  2  0.76' 
10  6  3  1.14' 
20  10  4  1.52' 
35  15  5  1.90' 
56  21  6  2.28' 
84  28  7  2.66' 
120  36  8  3.04' 
165  45  9  3.42' 
220  55  10  3.80' 
286  66  11  4.18' 
364  78  12  4.56' 
455  91  13  4.94' 
560  105  14  5.32' 
680  120  15  5.70' 
816  136  16  6.08' 
969  153  17  6.46' 
1140  171  18  6.84' 
1330  190  19  7.22' 
1540  210  20  7.60' 

4 sided 
#total  #base  #level  height 
1  1  1  0.38' 
5  4  2  0.76' 
14  9  3  1.14' 
30  16  4  1.52' 
55  25  5  1.90' 
91  36  6  2.28' 
140  49  7  2.66' 
204  64  8  3.04' 
285  81  9  3.42' 
385  100  10  3.80' 
506  121  11  4.18' 
650  144  12  4.56' 
819  169  13  4.94' 
1015  196  14  5.32' 
1240  225  15  5.70' 
1496  256  16  6.08' 
1785  289  17  6.46' 

6 sided 
#total  #base  #level  height 
1  1  1  0.38' 
8  7  2  0.76' 
27  19  3  1.14' 
64  37  4  1.52' 
125  61  5  1.90' 
216  91  6  2.28' 
343  127  7  2.66' 
512  169  8  3.04' 
729  217  9  3.42' 
1000  271  10  3.80' 
1331  331  11  4.18' 
1728  397  12  4.56' 

I also did you the favor of sorting them according to total number of cans. If you want to build one, and you know how many cans you have,
but don't know what size to shoot for, look it up on this table.
Pyramid Building Table 
#total  #base  #level  height  #sides 
4  3  2  0.76'  3 sided 
5  4  2  0.76'  4 sided 
8  7  2  0.76'  6 sided 
10  6  3  1.14'  3 sided 
14  9  3  1.14'  4 sided 
20  10  4  1.52'  3 sided 
27  19  3  1.14'  6 sided 
30  16  4  1.52'  4 sided 
35  15  5  1.90'  3 sided 
55  25  5  1.90'  4 sided 
56  21  6  2.28'  3 sided 
64  37  4  1.52'  6 sided 
84  28  7  2.66'  3 sided 
91  36  6  2.28'  4 sided 
120  36  8  3.04'  3 sided 
125  61  5  1.90'  6 sided 
140  49  7  2.66'  4 sided 
165  45  9  3.42'  3 sided 
204  64  8  3.04'  4 sided 
216  91  6  2.28'  6 sided 
220  55  10  3.80'  3 sided 
285  81  9  3.42'  4 sided 
286  66  11  4.18'  3 sided 

#total  #base  #level  height  #sides 
343  127  7  2.66'  6 sided 
364  78  12  4.56'  3 sided 
385  100  10  3.80'  4 sided 
455  91  13  4.94'  3 sided 
506  121  11  4.18'  4 sided 
512  169  8  3.04'  6 sided 
560  105  14  5.32'  3 sided 
650  144  12  4.56'  4 sided 
680  120  15  5.70'  3 sided 
729  217  9  3.42'  6 sided 
816  136  16  6.08'  3 sided 
819  169  13  4.94'  4 sided 
969  153  17  6.46'  3 sided 
1000  271  10  3.80'  6 sided 
1015  196  14  5.32'  4 sided 
1140  171  18  6.84'  3 sided 
1240  225  15  5.70'  4 sided 
1330  190  19  7.22'  3 sided 
1331  331  11  4.18'  6 sided 
1496  256  16  6.08'  4 sided 
1540  210  20  7.60'  3 sided 
1728  397  12  4.56'  6 sided 
1785  289  17  6.46'  4 sided 

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