Wouldn't the followiung work for a 2x2 square? R U D R L 0.1 5.3 (sum = 9) Tom Éric Angelini writes:
Hello MathFun The aim of this challenge is to fill a square (that has a 0 --zero-- in its upper-left corner) with integers. The best square is the one with the lowest sum of the said integers.
Here is my personal best for the 2 x 2 square (sum = 11):
0.1 6.4
... my best 3 x 3 has sum 63:
0.1.20 6.8.10 4.2.12
In order to fill a square, you have to start on the zero cell and jump: a) over zero cell (you land on 1 of the 4 adjacent cells – diagonal jumps are forbidden) b) from there, over 1 cell (you always have the choice to jump up, right, down or left if the landing cell is empty) c) from there, over 2 cells (same rules as above) d) from there, over 3 cells (same rules – at every step the size of the jump is increased by 1). etc.
Here is my path two fill the 2 x 2 square, starting on 0 (R=right, D=down, U=up and L=left; the size of the jump is increased by 1 at every step, the 1st jump being of size zero):
R D D U R L
Here is my path to fill the 3 x 3 square -- same convention:
R D R L D U L R L R U D L R D U D U R L
Can you beat my personal records? And find records for bigger squares?
(forgive me if this is old hat) (some illustrations here, on my personal weblog): https://cinquantesignes.blogspot.com/2019/05/jump-and-fill-my-square.html
Best, É.