Help with the name of a puzzle and the solution

My grandfather had this made of wood. I replicated it with my 3d printer. The object is to switch the big square with the horizontal rectangles by sliding the pieces. I don’t think i ever knew what it was called. Over the years I have forgotten the solution also. I can remember bits and pieces of it but not the correct order. Any help would be appreciated.

Dizzy Sailor

A dizzy sailor is standing on a 15×15 square tiled board. From their initial square they are able to move to any square sharing a common side. Due to the sailor’s dizziness, after every move they immediately make a left or right turn before repeating this process (that is, they are never able to enter and exit a square in a straight line). What is the largest number of squares the dizzy sailor can walk on if they are not allowed to repeat squares and the last step of their path must end at the square they started at?

Source: http://nyccami.org/what-do-you-do-with-a-dizzy-sailor/

Consecutive integer sequence

Find a consecutive integer sequence – n, n+1, n+2, …., n+k such that there does not exist a number in the sequence which is co-prime to all the other numbers in the sequence.

For example, 2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 is NOT such a sequence because 7 is co-prime to all the other numbers in the sequence.

[OC] A Game

https://drive.google.com/file/d/18OLhqqc5YQoP2NZUUIlpDj9R17xAzLcL/view

This is a html code for a game. It displays 10 numbers vertically with two buttons on either side of each number- blue and green. If blue button is clicked, The entire sequence from where it is clicked gets reversed. If the green button is clicked, That number is exchanged with the next number. Once the button is clicked, It will disappear. That is, Each button can be clicked exactly once. The goal is to arrange the numbers in ascending order using those buttons. Proving that it is always possible to arrange the numbers in ascending order, is also an interesting question…