because why not
picture a pyramid with n layers of cells with numbers
the first layer has 1 cell with a number (Let it be zero, its value isn't important)
each subsequent layer has 1 more cell (the numbers in these can be any whole positive number)
the last layer has n cells, of course.
now imagine you are at the top layer and you want to get to the bottom layer.
rules are: you can only go down (not from the second layer to the first layer again etc), and you can only go to one of the two immediate number cells under you.
as you go down you add up the value of each cell you pass through.
question is: how to determine the best path? i.e which path gives you the biggest sum?
the pyramid might look like this:
for example: the pyramid
1
3 5
obviously the best path is 1->5. totaling 6
the pyramid
0
1 0
1 0 6
here one would go 0_0_6 , 6 in total.
of course we can try all the paths and compare them , but this becomes stupidly hard as the number of layers grow.
the possible amount of paths is 2^(n-1) so a 7 layer pyramid has 64 paths. each of which is composed of n sums. so it is a lot of calculations to do manually
