The students in a school are having a cup stacking contest. John has a pyramid 9 layers high. How many cups will he need to add to his pyramid to increase the number of layers to 12?

The students in a school are having a cup stacking contest. John has a

1.	The students in a school are having a cup stacking contest. John has a pyramid 9 layers high. How many cups will he need to add to his pyramid to increase the number of layers to 12?
Answer» Please see the DOCUMENT enclosed. If the stacking is done as per that method, then we need, for a stack of L LEVELS, total number of CUPS at level L = L total number of cups for all levels from 1 to L : 1 + 2 + 3 + ... + L = L ( L + 1)/2 So the number of cups needed to increase the number of LAYERS to 12 from 9 is: 12(12+1)/2 - 9 (9+1)/2 = 78 - 45 = 33 ==================== Another method is: We need L more cups to increase the number of layers from L - 1 to L. Hence, we need, to go from level 9 to level 12: 10+11+12 = 33 cups more.