What are the maximum number of grape vines that can be planted, not closer than nine feet apart, in a square plot containing one-sixteenth of an acre?
(Note: each side of this square plot would be 52 feet 2 inches)
(Note: each side of this square plot would be 52 feet 2 inches)
Our Solution:
By drawing a line on the bias as shown in the adjoining diagram, from one corner to another, and crossing and paralleling the same, it will be found that 41 vines can be planted, a little over nine feet apart, and well within the fence line.
HOWEVER, Peter Noll has found a better solution: 44 grape trees
This comes about by planting 6,5,6,5,6,5,6,5 trees in 8 layers with horizontal spacing 10.433 feet and layer distances 7.45 feet. Any 3 adjacent trees form a triangle with side lengths 10.433, 9.097, 9.097 feet.
HOWEVER, Peter Noll has found a better solution: 44 grape trees
This comes about by planting 6,5,6,5,6,5,6,5 trees in 8 layers with horizontal spacing 10.433 feet and layer distances 7.45 feet. Any 3 adjacent trees form a triangle with side lengths 10.433, 9.097, 9.097 feet.
do you know?
ReplyDeleteDuring the Ukrainian puzzle championship a maximal known solution with 46 vines was found (see more info and diagram on http://www.ageofpuzzles.com/Publications/PuzzleClassicsAtG4G7/PuzzleClassicsAtG4G7-SOLS.htm)