How many three-digit natural numbers are there such that the sum of these is equal to 24?

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If all the digits are less than 8, the sum will be less than $3 \times 8=24$.

If one of them is equal to 8, the sum of the other two will be 16 and we have the possibilities: $16=8+8=7+9$. We then obtain seven solutions: 888, $789,798,879,897,978$ and 987.

If one of the digits is equal to 9, the sum of the other two will be 15 and we have the possibilities: $15=7+8=6+9$. The first equality leads to solutions already found. The other results in the numbers 699, 969, and 996.

There are then ten natural numbers with the desired property: 888, 789, $798,879,897,978,987,699,969$ and 996.