She likes 1600
225 = 15^2......like
224 = 15^2 - 1^2..no
900 = 30^2 ...like
800 = 30^2 - 10^2 no
144 = 12^2 ....like
145 = 12^2 + 1^2 no
1600 = 40^2 ...........
1700 = 40^2 + 10^2
According to the trend she must like 1600
Its - 1^2, -10^2, +1^2, then +2^2 she doesn't like