Enigma 266: Twelve trees
18 March 2015
Posted by on
From New Scientist #1413, 7th June 1984 [link]
The dots are very thin vertical trees, laid out on an endless square grid, with each tree a kilometre from its nearest neighbours. The two circles are Sue’s first attempts at drawing the smallest and the largest possible circles which enclose exactly 12 trees. The smaller has a radius of 1803 metres, the larger of 2061 metres. Given that the centres can be anywhere you like, that the radius must be an exact whole number of metres, and that the circles must not pass through any tree, can you do better? What in fact is:
(a) the smallest possible radius?
(b) the largest possible radius?
for such a circle enclosing exactly 12 trees?