Give the first two solutions of the n-Queens problem for n = 6 Write it in the form (1,2), (2,2), (3,2)

(1,2), (2,4), (3,6), (4,1), ( 5,3), (6,5)

Step-by-step explanation:

Given the first two solutions of the n-Queens problem for n = 6

The solution requires that no two queens share the same row, column, or diagonal and each variable lies in the domain [1,6] (6 rows).while finding a solution we must ensure that no two queens are not placed on the same row and in the same diagonal

hence the first two solutions can be expressed as :

(1,2), (2,4), (3,6),(4,1),( 5,3), (6,5)

i hope this is what you were looking for.

see attached graph

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4