Question 1
The source example places a chain of consecutive positive integers in a $4\times4$ grid: $1\to2\to3\to4\to5\to6$, with successive distances $1,2,1,2,1$.
Starting with 1 in the top-left cell, construct the longest possible chain with distances $1,2,1,2,\ldots$ alternately. What is the largest number that can be placed in (i) a $4\times4$ grid, and (ii) a $5\times5$ grid? Draw an example for each.
Starting with 1 in the top-left cell, construct the longest possible chain with distances $1,2,1,2,\ldots$ alternately. What is the largest number that can be placed in (i) a $4\times4$ grid, and (ii) a $5\times5$ grid? Draw an example for each.