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Ball Drop

Well, if we want to get nerdy about it... It actually depends on the weight of the bowling ball. Bowling balls of less than about 12 lbs will float in seawater and those which are greater will sink. Regulation golf balls sink in seawater. If the bowling ball is less than 12 lbs, the golf ball will hit the 'ground' first... But wait!! A floating bowling ball might get transported to shore before the golf ball makes it to the sea floor! Too many variables :)

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Multiples of 8 plus 1

A little Python code to illustrate the proof:

# Import Pylab:

from pylab import *

m=0 c=0 k = [1,3,5,7,9,11,13,15,] for x in k: m=m+c c=c+1 n=m8+1 print (x,'^2 = 8 ',m,'+ 1','=',n) print ('The multiple of 8 increases by the sequence 0,1,3,6,10, etc...') print ('In other words: 1, then 2, then 3, etc... is added to the multiple at each iteration.')

Execute:

1 ^2 = 8 * 0 + 1 = 1 3 ^2 = 8 * 1 + 1 = 9 5 ^2 = 8 * 3 + 1 = 25 7 ^2 = 8 * 6 + 1 = 49 9 ^2 = 8 * 10 + 1 = 81 11 ^2 = 8 * 15 + 1 = 121 13 ^2 = 8 * 21 + 1 = 169 15 ^2 = 8 * 28 + 1 = 225 The multiple of 8 increases by the sequence 0,1,3,6,10, etc... In other words: 1, then 2, then 3, etc... is added to the multiple at each iteration.

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All the King's Wine

Can be solved with matricies in similar fashion to the given solution... If I get around to making the code, I'll post it!

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