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Extreme speed stack

Extreme speed stack

In recent years, a sport called Speed ​​stack. The game consists of stacking pyramid-shaped glasses making different series of 3, 6 or 10 glasses according to the game mode. You can watch this illustrative video.

A young man from that country is willing to break the height record of stacked glasses and wants to make a pyramid of 100 tall glasses. To do this you will use a platform that allows you to reach as high as necessary.

Do you know how many glasses you will need to accomplish your feat?

Solution

Each level of the pyramid contains one more glass than the previous one. So the upper level will have only one glass, the next level will have 2 and so on to the base of the pyramid that will have 100 glasses. So the total number of glasses you will need is obtained from the sum of glasses of all levels:

1 + 2 + 3 +… + 100 = (n2 + n) / 2 = (1002 + 100) / 2 = 5050