The above image shows the reconstructed path of the knight. The move count of 50 (and region sum of 75) can be deduced using three observations:

• the sum of all numbers must be a triangular number,
• the sum of all numbers must be divisible by the number of regions (17), and
• the regions of size 2 must have an odd sum by parity arguments of knight moves.

Once this is known the path of the knight can be deduced by hand or with the aid of a program (we saw both solution methods). The sum of the squares of the maxima of each row comes to 14820.

Congrats to this month’s solvers who successfully deduced the knight’s path!