"The number of Xs" - why no article?

Looking at Why not add ‘the’ before the last ‘steps’ word? as recently asked on ELL, I was struck by the realisation that it’s very difficult to find contexts where we would include both articles in noun phrases of the general form the number of the [things, steps, whatever]. But there’s no such restriction with other "attributes", such as the colour of the steps, the size of the steaks, the age of the mountains,…

1: Find the average length of words in this sentence (fine)
2: Find the average length of the words in this sentence (also fine)
3: Find the number of words in this sentence (fine)
4: Find the number of the words in this sentence (DOESN’T WORK)

Is there any identifiable reason why number should work like this? Are there any other "attribute" words (apart from number and near-synonymous quantity) that are similarly "averse" to being attached to a plural noun phrase prefaced by the definite article?