> IMHO you should memorize one very strong password for one somewhat-trustworthy site.
This would be necessary if one is using a password manager, which is something everyone should use for multiple reasons and benefits.
As an alternative, you could also invent a scheme for passwords. Have a prefix, body and suffix for every password. You decide which ones should be static and which ones should be something that's easy to derive just by looking at the website name (part of the name, few letters from specific positions). You can also have different static pieces based on the nature of the site - email vs. bank vs. online store. This may not be as good as using a unique password per site that's a random strong password generated by a password manager, but is easy to remember depending on how you construct it.
This would be necessary if one is using a password manager, which is something everyone should use for multiple reasons and benefits.
As an alternative, you could also invent a scheme for passwords. Have a prefix, body and suffix for every password. You decide which ones should be static and which ones should be something that's easy to derive just by looking at the website name (part of the name, few letters from specific positions). You can also have different static pieces based on the nature of the site - email vs. bank vs. online store. This may not be as good as using a unique password per site that's a random strong password generated by a password manager, but is easy to remember depending on how you construct it.