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"typical modern book " means:

  1. It's a modern book and hardly uses ancient languages or any topolects.
  2. It's something like a famous novel(not a short story) or book with a high reputation. 
  3. It's a normal book, not a dictionary or technique book.

Additionally, I wonder how many distinct characters can cover 99.7% of the
book content.

The source of the problem is that I want to know how many unstudied (the
meaning of) kanjis I will meet when reading a book.
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question
words kanji
How many distinct kanjis or words are there in a typical modern Japanese book?
There are currently [2136
常用漢字](https://en.wikipedia.org/wiki/J%C5%8Dy%C5%8D_kanji). However, using
writers will often use 漢字 outside of this list.

So I ran a script to calculate the total number of unique 漢字 in _Harry Potter
and the Chamber of Secrets_ (a modern novel mentioned there) and on ノルウェイの森/
_Norwegian Wood_ (a "famous" Japanese language novel, though perhaps not
"typical") and compared it to the 常用漢字 list. You can see some of the code (it
just has the results for the distinct values in the books)
[here](https://repl.it/repls/TomatoAgreeableQuote). Here's what I got

_Harry Potter and the Chamber of Secrets_ : 206 non-常用漢字 out of 1768 漢字 (肱
might be a typo for 肘, 躯 for 体, 荊 for 茨, and 綴 for 絞. I also wonder if 姐 and 嬉
are old forms or my source text has typos. I also have no clue about 杵 and 磔,
which are likely wrong. I'll try to confirm with a physical copy in the
future.)

> {'蘇', '捌', '曾', '鈎', '撫', '剥', '捷', '篭', '恰', '鍮', '撒', '涎', '虱', '樽', '炸',
> '塵', '椀', '吼', '淀', '絢', '歪', '掠', '瞥', '揉', '眩', '董', '錆', '嘘', '楊', '蝶',
> '靄', '疼', '呆', '叱', '弛', '攣', '棍', '猾', '藁', '軋', '荊', '揃', '纏', '甥', '這',
> '樫', '苺', '掻', '惚', '杖', '煤', '咳', '煽', '辻', '瓢', '詫', '捺', '脛', '溢', '溜',
> '蝋', '鎧', '糞', '芻', '腿', '噛', '唸', '痺', '鍔', '霞', '狡', '翠', '昂', '罠', '燭',
> '蜘', '牢', '躯', '叩', '杵', '雛', '佇', '鳩', '呟', '灼', '爛', '逢', '嘴', '黴', '呑',
> '兎', '嘩', '濡', '轟', '鞄', '咎', '棘', '笥', '壷', '閃', '猜', '楓', '聡', '麿', '箪',
> '捧', '馴', '藹', '蛙', '肱', '馳', '覗', '釘', '茜', '埃', '愕', '雀', '皺', '躇', '鋸',
> '踝', '穣', '奢', '檻', '箒', '姐', '甜', '嵌', '萄', '螺', '嬉', '唖', '秤', '仔', '掴',
> '窪', '狼', '翔', '綴', '腔', '箔', '芍', '躊', '鮭', '磔', '鱗', '悶', '禿', '躓', '蛛',
> '惹', '閂', '哮', '瓜', '腑', '曙', '槌', '沫', '狐', '倦', '卿', '剃', '栗', '燻', '頷',
> '憑', '斧', '蟻', '橙', '竿', '怯', '紐', '穢', '耽', '尖', '咆', '凱', '蒼', '肋', '錘',
> '踵', '窩', '縞', '竪', '痙', '鞭', '吊', '喧', '聳', '髭', '焚', '廻', '斐', '堵', '頬',
> '醇', '瘤', '鋏', '葡', '〇', '鉤', '鷲', '漉', '舐', '滲', '堰'}

ノルウェイの森/ _Norwegian Wood_ : 167 non-常用漢字 out of 1746 漢字 (Like before 姐 and 嬉
might be old forms/typos. I'll try to confirm with a physical copy in the
future)

> {'梯', '遙', '鱸', '鎧', '梢', '徨', '撞', '喧', '昂', '雀', '而', '鳩', '庇', '轟', '燈',
> '葡', '拗', '函', '禿', '悶', '槌', '訊', '紐', '碗', '鞄', '鮭', '蝕', '蛙', '軋', '舐',
> '檻', '湘', '茗', '萄', '蓮', '鯵', '綺', '裳', '癬', '胡', '吠', '縞', '詫', '洒', '樵',
> '奢', '掻', '痰', '爛', '呑', '姐', '錆', '疥', '殆', '糊', '〇', '駕', '罠', '夾', '頬',
> '淋', '蝿', '楊', '鴉', '歪', '篇', '睨', '吊', '疼', '叩', '嚢', '噛', '咳', '睾', '竪',
> '唖', '菱', '濡', '囁', '仄', '糞', '蹙', '脆', '稜', '彷', '褪', '漕', '蟻', '曝', '栗',
> '釘', '杖', '柏', '螢', '甥', '旭', '剃', '耽', '惣', '愕', '癌', '喰', '掴', '醤', '嘘',
> '嘔', '顰', '腿', '疇', '瑞', '蹟', '嬉', '馴', '蝉', '垢', '鯛', '桐', '弘', '挪', '嘩',
> '釆', '揃', '云', '撫', '玲', '屑', '噌', '怯', '噂', '這', '桶', '鰻', '髭', '迂', '蛾',
> '蝶', '瓜', '巳', '鱈', '苔', '苑', '綜', '瞞', '墟', '阿', '辿', '茫', '睥', '茸', '樫',
> '蠅', '鼠', '弛', '坦', '穢', '倦', '鹸', '椀', '凌', '眩', '伊', '鴨', '叱', '煉', '苺',
> '捧', '劫'}

If we include [人名用漢字](https://en.wikipedia.org/wiki/Jinmeiy%C5%8D_kanji),
which brings the total 漢字 to 2999, _Harry Potter and the Chamber of Secrets_
has 104 that aren't in either list and ノルウェイの森/ _Norwegian Wood_ has 78.

> {'姐', '呟', '壷', '嘘', '鍮', '咆', '呆', '爛', '滲', '瘤', '掴', '肱', '咳', '憑', '穢',
> '髭', '叩', '禿', '塵', '吼', '腿', '炸', '痺', '篭', '皺', '猾', '噛', '蜘', '藹', '舐',
> '腑', '頬', '甜', '揉', '黴', '芍', '愕', '煽', '罠', '閂', '聳', '檻', '眩', '燻', '鈎',
> '嵌', '吊', '痙', '唸', '糞', '咎', '捌', '歪', '攣', '剃', '脛', '蟻', '踵', '荊', '虱',
> '怯', '蛛', '奢', '蝋', '棍', '靄', '掻', '窩', '〇', '佇', '頷', '躯', '哮', '笥', '躊',
> '漉', '躓', '箒', '叱', '嘴', '芻', '鍔', '剥', '鋏', '躇', '埃', '箪', '涎', '棘', '疼',
> '呑', '狐', '猜', '鉤', '踝', '狡', '鮭', '磔', '唖', '軋', '悶', '覗', '蛙', '牢'}
>
> {'拗', '囁', '褪', '彷', '唖', '蹙', '眩', '鰻', '睥', '蠅', '嘔', '愕', '徨', '禿', '鮭',
> '咳', '疥', '鱈', '髭', '疇', '蛙', '釆', '癌', '醤', '洒', '顰', '鼠', '樵', '〇', '蝕',
> '鹸', '掴', '呑', '爛', '癬', '螢', '吠', '吊', '蝿', '頬', '悶', '睾', '蟻', '糞', '叩',
> '怯', '掻', '疼', '茫', '夾', '穢', '垢', '叱', '蛾', '鱸', '歪', '鯵', '睨', '軋', '瞞',
> '舐', '蝉', '罠', '茗', '脆', '奢', '腿', '挪', '嚢', '檻', '鴉', '仄', '嘘', '噛', '痰',
> '姐', '墟', '剃'}

As for your second question as to how many 漢字 you need to know to know 99.7%
of the ones used, I used the results of this [Github
repository](https://github.com/scriptin/kanji-frequency) to get the following:

> [Aozora Bunko](https://www.aozora.gr.jp/) (there are many many "old"
> stories): 3820
>
> News (June 2014 - June 2015, more samples from 2015, from 4 different
> sources. Only article titles, subtitles, main text body and image captions
> were scanned. Weather forecasts and area-specific news were not included). :
> 2007
>
> Wikipedia (a wikipedia dump: 2835
>
> Twitter (steaming data for 1 week): 2312

Also according to [this
analysis](http://web.archive.org/web/20080320143000/http://nozaki-
lab.ics.aichi-edu.ac.jp/nozaki/asahi/kanji.html) of 朝日新聞朝夕刊's paper through
the entirety of 1993, you need to know 1977 to be able to understand 99.7%.
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answer
This answer does not contain the exact information you are requesting but
maybe it'll be useful to you anyway. I am not aware of any online resource
that includes data from modern publications (such a resource would probably be
very difficult to compile due to copyrights and the like).

The data below is from the same source as the one I used to answer this
question - "[Which is the most popular non-Jōyō
kanji?](https://japanese.stackexchange.com/questions/61905/which-is-the-most-
popular-non-j%c5%8dy%c5%8d-kanji/61907#61907)". The data includes frequency of
appearance data for kanji from 4 resources, Aozora Bunko, Wikipedia,
Newspaper, and Twitter. Aozora Bunko might be close to what you want but I
believe that the bulk of its corpus is older text which might not reflect
modern frequencies.

The tables show the number of kanji that cover a given fraction of total kanji
from each source.

**Wikipedia**  
0.745 -------- 649  
0.795 -------- 792  
0.845 -------- 981  
0.895 -------- 1228  
0.945 -------- 1588  
0.975 -------- 2093  
0.985 -------- 2492  
0.997 -------- 3529  

**Aozora Bunko**  
0.75 -------- 570  
0.80 -------- 711  
0.85 -------- 902  
0.90 -------- 1181  
0.95 -------- 1657  
0.975 ------- 2248  
0.99 -------- 2657  
0.997 ------- 3714  

**Newspaper**  
0.75 -------- 658  
0.80 -------- 789  
0.85 -------- 958  
0.90 -------- 1185  
0.95 -------- 1566  
0.975 ------- 1997  
0.99 -------- 2424  
0.997 ------- 3292  

**Twitter**  
0.75 -------- 592  
0.80 -------- 710  
0.85 -------- 896  
0.90 -------- 1151  
0.95 -------- 1464  
0.975 ------- 1970  
0.99 -------- 2347  
0.997 ------- 3409  

The 2136 Jouyou kanji cover the following fraction of the 4 databases
(backward order so they line up)

0.9815 ------ Wikipedia  
0.9399 ------ Aozora  
0.9914 ------ Newspaper  
0.9831 ------ Twitter
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answer