Arithmetic Progressions

arrange a multiset of digits into an arithmetic progression(a sequence of numbers which differ by the same amount called the common difference).

You're scored based on the length of your sequence. Get one less than the target length to clear the level, match it to get a gold star, or beat it to get a purple star (I don't know if a longer sequence exists for all the levels).

press the hint button to find out the common difference, use space to create new terms, backspace to delete the selected term and z to undo you moves.

this game was a spur of the moment idea i got when i was staring at digit-shaped fridge magnets , which someone had arranged into an AP but without using all the digits, i then tried to make an AP which used all of the digits but couldn't think of one. But there are many interesting questions to ask here, for example given a random multiset of N digits is there an easy way to prove that you can't make an (non-trivial)AP that uses all the digits? or given a finite length AP can you rearrange the digits to make a longer AP, or is the length of that AP maximal?(this is the inspiration for the purple stars so please comment the answer if you get one). if you have any thoughts about these questions feel free to share them in the comments, and thank you for playing the game or reading this text.