# Maths Mate Sheet 6 Question 23 (Term 4 2014)

Prediction: I predict this question will be about addition because of the repeated pluses in the question.

Read: The dight sum for 195 is 1 + 9 + 5, or 15. The digit sum for 200 is 2 + 0 + 0, or 2. Find the two consecutive numbers that have the digit sums of 27 and 1.

Clarification: None needed.

The Big Question: Find the two consecutive numbers that have the digit sums of 27 and 1.

Mathematician’s Toolbox: Work backwards/Have I seen a similar problem?

Solving: Firstly I figured out what the factors of 27 were 1,3,9, and 27. That means 999 was the first number because 3 times 9 is 27 and 999 has 3 9’s in its digit sum. Since the numbers must be consecutive I figured 1000 was the second number because it has the digit sum of one and it’s consecutive.

Conclusion: So the answer was 999 and 1000