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I bet this on the first go, without thinking of an in-depth heuristic. Maybe I was lucky, but it doesn't seem to hard.

I struggled with this version, which is kind of similar: http://joezeng.github.io/144/

Not beat yet, but I don't think it is possible to algorithmically.

144=3 x 48 ; 48=3 x 16

16 is 'easy' to create - if you can avoid creating any three-pairs.

The trick of this game is that you can have 3,4,5 pairs. There may be some ways to choose 4 and 5 pairs along with the easier 2 and 3 pairs to win it - my efforts so far with the simple strategy produced two 48 pairs, and a seemingly random chance at producing an elusive third 48th pair, so any solution I would think would be considerably more difficult, if one exists at all.

Yeah, this one doesn't seem so hard. Variants like 144 are a challenge because you can fill the board with tiles that can never lead to your goal, and it's easy to get into a situation where you can't help generating them.

I thought I'd ask for a goal 3^6 (729). But this is impossible with this algorithm.

243 243 243 x x

81 81 81 x x

27 27 27 x x

9 9 9 x x

3 3 3 x x

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