Maybe these kanji puzzles fit your description better, particularly the first row of puzzles: 漢字しりとり, 穴埋め and 漢字分割推理.
漢字しりとり (Kanji shiritori)
Rules
The goal of this first puzzle is to connect all but two characters into a long kanji shiritori train consisting of words that are at least two kanji characters long. The two kanji that are not connected then form the solution to the puzzle.
Note that the reading of a kanji character can differ from link to link, the character has to be compatible, not its reading.
Solution
Here, the shiritori chain is as follows:
START (top left) → 面談 → 談話 → 話題 → 題目 → 目論見 → 見聞録 → 録画 → 画面 → 面白 → 白骨 → 骨格筋 → 筋力 → 力仕事 → 事業家 → 家庭科 → 科目 → GOAL (bottom right)
The two characters that are not connected are:
体 and 車
The solution therefore is:
車体 because 体車 doesn't exist
穴埋め (Fill in the gap)
Rules
The aim in this puzzle is to find the central kanji such that CENTRE + RIGHT, CENTRE + BOTTOM, LEFT + CENTRE and TOP + CENTRE are all valid two-character compounds. Again, reading is not important here, only the fitting kanji.
Solution
The solution to this puzzle would be:
愚
With the valid compounds:
愚痴, 愚行, 暗愚 and 凡愚
漢字分割推理 (Partial kanji)
Rules
For this puzzle, two or more kanji characters that form a valid compound are partially shown in a square grid. The solution to the puzzle is the compound that comprises the partially visible kanji.
Solution (easy puzzle)
The partially visible kanji are:
Left: 面, right: 書
The solution therefore is:
書面 because 面書 is not a valid compound
Solution (hard puzzle)
The partially visible kanji are:
Top left: 効, top right: 果, bottom left: 相, bottom right: 乗
The solution therefore is:
相乗効果