It was called Push Box (aka: Sokoban) in pc version back 12-13 years ago. There were only 100 levels then, but the game has a high replayable value, as you can attempt to solve it again with minimum moves to achieve the three stars status, plus, you’d probably forget the solutions after just a few months.
Five years ago, I was overjoyed to discovered this game in the App Store. Not only it has the original 100 levels (set #4), but an additional of almost 1300 new levels, with some repeats. I have been working on my iPad since and completed about 5 sets before more were added to a total of over three thousands after about a year, then gradually to 4000+, eventually to 6000+. Recently, another update made that to a total of 8000+ levels. At this rate, I’ll be retired before I solve them all, that is, if the creator does not add even more.
The only written review did not seem to appreciate this game much (at the time), which is ok, we all have our preferences, but thanks to his review, I think, the creator went on to created a whole lot more levels. Many of which seem utterly Impossible, which can be discouraging at times, but if you are patient and willing to keep trying, the feeling of solving a challengingly difficult, impossible looking level (there are tons) on your own is rather rewarding. Many of them were cleverly designed in my opinion. Changes have also been made to ensure you don’t lose your progress on the level you are currently working on, as they have in the past after you recharge your device, which shows that the creator pays attention to feedbacks.
I wholeheartedly recommend this game, even though it may not be your cup of tea. Give it a try if you enjoy a good puzzle game (did I mention it’s free?) There are some versions that charges you 1 cent per back move (you’ll be surprise those back moves add up real fast)! The only thing you have to pay is the solutions, which is still cheaper then those back moves, but I’d would try to get the three stars status first. It’s also good for preventing dementia!