# What 5,500 Knuth exercises look like

> How many exercises are in TAOCP Volumes 1 to 4B, how hard they are, how many Knuth recommends, and which ones the cracked.guide path picks for you.

By Dane Dolph. Published 2026-10-20 on the cracked.guide blog.

Volumes 1 to 4B of The Art of Computer Programming hold about **5,500 exercises**, by the counts in our reading guides, rated from 00 (do it in your head) to 50 (unsolved research). A bit over a quarter carry Knuth's triangle for "recommended". Nobody does them all. Here is what the pile looks like and how we chose from it.

## The counts

| Volume | Exercises | Recommended (▶) | Rating range |
| --- | --- | --- | --- |
| [Vol 1](https://cracked.guide/taocp/volume-1) | 932 | 273 | 00 to HM50 |
| [Vol 2](https://cracked.guide/taocp/volume-2) | 918 | about 240 | 00 to HM50 |
| [Vol 3](https://cracked.guide/taocp/volume-3) | 964 | 217 | 00 to M50 |
| [Vol 4A](https://cracked.guide/taocp/volume-4a) | 1498 | 452 | M00 to 50 |
| [Vol 4B](https://cracked.guide/taocp/volume-4b) | 1202 | 387 | 01 to HM49 |
| **Total** | **5514** | **about 1,570** | |

These come from the review week of each volume in our guides, which counted every section the path covers. Volume 4B's count includes the 147 exercises of its Mathematical Preliminaries Redux.

## What the ratings mean

A 10 is a minute of thought. A 20 is fifteen or twenty minutes. A 30 can be an evening. A 40 is a term project, and a 50 was an open research problem when it was written. M means math, HM means math beyond the book, and the triangle means Knuth recommends it. [The full explanation](https://cracked.guide/learn/knuth-exercise-ratings).

## What we picked

Every Knuth section on the path has a reading guide with an exercise list: specific numbers with their ratings and a line on why each is worth the time. Across the five volumes the guides pick about 980 exercises, under a fifth of the total. Picks were only listed where the number, rating and content were certain; where they were not, the guide gives advice instead of guessing.

The idea is a steady diet: the easy ones in your head, a few recommended ones on paper, one stretch problem a week. Each review week adds a mixed set you have not seen, for the exercises you skipped.

## Logging what you solve

On each guide page you can log the exercises you work: tick a picked one, or add any number from the book, with its rating and how far you got. Over a few months the log shows you something motivating: a growing number of solved 20s and 30s that would have looked impossible in week 29. Start with [§1.1, Algorithms](https://cracked.guide/guide/knuth-w017-0), which has nine friendly exercises.

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Source: https://cracked.guide/blog/what-5500-knuth-exercises-look-like
cracked.guide: A free, dated 145-week path to getting genuinely cracked at programming.