1. 困
  2. 难

困

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Meta:

  1. 困 is the 866th most frequent character.
  2. 困 has 2 dictionary entries.
  3. 困 appears as a character in 19 words.
  4. 困 appears as a component in 7 characters.

Decomposition:

Once :
困 => 囗, 木
Radical :
困 => 囗 (enclosure), 木 (tree)
Graphical :
困 => 冂, 一, 一, 丨, 八

Pinyin & Meaning:

  1. kun4 - to trap/to surround/hard-pressed/stranded/destitute
  2. kun4 - sleepy/tired

Pronunciation Clues:

  1. There are no phonetic clues for this character.

Example Words:

High Frequency

困 

Medium Frequency

困境 
困惑 
困扰 (困擾)
困难 (困難)
贫困 (貧困)

Appears In:

困 also appears in:
捆阃悃硱睏綑稇

难

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Meta:

  1. 难 is the 295th most frequent character.
  2. 难 has 2 dictionary entries.
  3. 难 appears as a character in 118 words.
  4. 难 appears as a component in 4 characters.

Decomposition:

Once :
难 => 又, 隹
Radical :
难 => 又 (right hand), 隹 (small bird)
Graphical :
难 => ㇇, ㇏, ㇒, 丨, 一, 二, 丨, 一, 丶

Pinyin & Meaning:

  1. nan2 - difficult (to...)/problem/difficulty/difficult/not good
  2. nan4 - disaster/distress/to scold

Pronunciation Clues:

  1. There are no phonetic clues for this character.

Example Words:

High Frequency

困难 (困難)
难 (難)
难以 (難以)
难受 (難受)
难得 (難得)
难过 (難過)
难道 (難道)

Medium Frequency

患难 (患難)
灾难 (災難)
为难 (為難)
磨难 (磨難)
艰难 (艱難)
苦难 (苦難)
难免 (難免)
难吃 (難吃)
难堪 (難堪)
难度 (難度)
难得一见 (難得一見)
难忘 (難忘)
难怪 (難怪)
难为 (難為)
难看 (難看)
难听 (難聽)
难处 (難處)
难关 (難關)
难题 (難題)

Appears In:

难 also appears in:
滩摊瘫傩
Decomposition Levels:
Level 1: Only divided once. So only two components.
Level 2: Radical Decomposition. The character gets decomposed into its lowest radical components. For the complete list visit the Radical wikipedia page.
Level 3: Graphical Decomposition. Shows all the strokes & lowest level of components that make up the character.
If you see questions marks or too many "block" characters, especially when it comes to level 3 decomposition you might need the correct font.