Equals Times

Exercise 10.4 Suppose, supppose, if you pppplease, that pppppiles of ppppppeas fall on Pppppppeater's pppppppplate. (Let's idealize his ppppppppplate to an infinite pppppppppplanar grid). All the pppppppppppeas ppppppppppppile onto one central square. As soon as there are enough pppppppppppppeas in one square to toppppppppppppple to each lower adjacent square while still remaining equal or greater in value, the ppppppppppppppeas will do so.

Exampppppppppppppples:

Code:

0 0 0
0 5 0
0 0 0

becomes

Code:

0 1 0
1 1 1
0 1 0

Code:

0 2 0
2 7 0
0 0 0

becomes

Code:

0 3 0
3 3 1
0 1 1

a. If each pppppppppppppppea is a cm cube, how many ppppppppppppppppeas will there be when the center pppppppppppppppppile is 1 km tall?


b. If Ppppppppppppppppppeter ppppppppppppppppppplaces one ppppppppppppppppppppea every second, I typppppppppppppppppppppe one word pppppppppppppppppppppper second, and the pppppppppppppppppppppppropppppppppppppppppppppppportion of words with ppppppppppppppppppppppppp in them is apppppppppppppppppppppppppproximately the same as in this ppppppppppppppppppppppppppproblem, how many total pppppppppppppppppppppppppppps will I have typpppppppppppppppppppppppppppped during the pppppppppppppppppppppppppppppperiod Pppppppppppppppppppppppppppppppeter sppppppppppppppppppppppppppppppppends ppppppppppppppppppppppppppppppppplacing his 1 km
ppppppppppppppppppppppppppppppppppile of
pppppppppppppppppppppppppppppppppppeas?