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I'm interested in the first stroke of characters like 司, 习, and 可. This is how it looks on my computer (but I don't know if this is a matter of fonts):

  • 可 starts off with a single horizontal stroke, whereas
  • 司 and 习 do not (it starts off horizontal, then proceeds downwards, then hooks).

My handwriting of 可以, 学习, and 司机 (where I've deliberately used the two "styles"):

可以, 学习, and 司机

I'm not sure if it's simply wrong to write this, or if they're acceptable alternatives.

Question: Do characters like 司, 习, and 可 have different first strokes?

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I'm not sure if it's simply wrong to write this, or if they're acceptable alternatives.

It's simply wrong. 横折勾 does not equal to 横 + 竖折勾. Even in artistic or decorative writing, they are clearly distinguished for the most of the time.

The answers about stroke order (笔顺) are not what was asked here.

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We can use zdic's 笔顺 for this:

フ一丨フ一

フ丶一

一丨フ一丨

So technically 司 and 习 begin with a 折 stroke, while 可 begins with a 横 stroke.

笔顺 works like:

笔顺名称 一(横) 丨(竖) 丿(撇) 丶(点) 乛(折)

笔顺编号 1 2 3 4 5

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The link has been provided to you for your reference in another answer.

However, there is a generic rule which I think it's good for you to know.

This is the one from the web:

新编笔顺规则歌诀

  从上到下为主,从左到右为辅。

  中央凸出先写,右上有点后补。

  横竖交叉先横,撇捺交叉捺收。

  上包下时先外,下包上时先内。

  三框首横末折,大口后封底部。

  多重复合结构,根据层次分组。

  特殊不合规则,源于从草从古。

  熟记规则特例,笔画正确无误。

  写字流畅美观,检字准确迅速。

I personally:

先上后下, 先左后右, 先中间后两边, ...

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