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We looked at a typical page of Maslanka puzzles from the Guardian Weekly, and concentrated on #3 here.
Puzzles 334 and 336 from Math Horizons Vol. 23, No. 3 (2016) This is puzzle 336 from Math Horizons showing first, second, third step in the above.
We chose the Collatz-like Problem 338. Based on experiments, we conjecture that starting with any number leads into a repeating loop…
We looked at three puzzles, and chose Problem 346. After some experiments, we conjectured that the only square in the list is 9, and tried expressing numbers like $88889$ in several different ways, starting from $999=10^4-1$.