You are on an infinite Cartesian plane at the origin (0,0). For every integer pair of coordinates (n,m) there's a null-dimensional point (that is, the point has zero width and height).
Some of these are "visible" to you, but some others are "invisible". For example, the point (2,2) is not visible from the origin since it is "blocked" by (1,1). On the other hand, (3,5) is "visible" to you since there are no other points in the way.
Where can you build an "invisible" unit (1x1) square (all four vertices of which are "invisible" points) as near as possible to you - and the origin?
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Submitted by maskass
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Rating: 4.0000 (5 votes)
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Solution:
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One such square has the vertices:
(14, 20), (15, 20), (14, 21), (15, 21).
The idea is that we need to find two pairs of consecutive integers that are multiples, collectively, of four distinct primes.
The primes that yield the lowest solution, of course, are the four lowest primes: 2, 3, 5, and 7.
The lowest pairs of consecutive numbers that are multiples of these primes are 14, 15 and 20, 21.
DJ offers a full solution and explanation here. |
