The solution is not too difficult: White must stop Black from disentangling his pieces, which means that he must keep the knight on d2 pinned while finding a way to approach with his queen. Once you have found the first move, which unblocks the d-file, the rest goes like clockwork: 1.Bb1! Kd1 2.Qd6 Kc1 3.Qf4 Kd1 4.Qd4 Kc1 5.Qe3 Kd1 6.Qd3 Kc1 7.Qc2 mate.
The real fun comes in the second part of Dawson's puzzler: if the board is extended to the right and upwards, and each square has sides of one inch, how far away must the queen be in the starting position for the problem to be a mate-in-69?
Dawson's answer: on the moon! If you work out the length of the ever- growing swings of the white queen, you will see that she doubles her distance from d2 every two moves. So she'll close in from 234 inches away in 68 moves. (One more move is then needed to give mate). There are approximately 216 inches in a mile, so for a mate in 69, she must begin 218 miles away - as far as the moon.