The document discusses the concept of digit sums, illustrating how to calculate them using a given number, specifically focusing on finding the largest two-digit number less than 100 with a digit sum of 11 (answering 92). It also introduces patterns associated with digit sums for both two-digit and three-digit numbers, culminating in the findings related to equations that describe these patterns. The content encourages further exploration of these mathematical patterns with other numbers.

1. MATHS FUN WITH DIGIT SUMS
The digit sum of a given number is the sum of all the digits of that
number e.g.,
The DIGIT SUM of
12345 = 1 + 2 + 3 + 4 + 5 = 15

2. Q. Find the biggest number, less than 100,
whose DIGIT SUM is 11?
First let’s look at the pairs of numbers that add up to 11.

3. Q. Find the biggest number, less than 100,
whose DIGIT SUM is 11?
Let us now use each pair to get a possible answer.

4. We can see that 110 and 101 won’t work because their digit sums are 2 (1 + 1 + 0).
Our answer is therefore 92.

5. But my mind would not stop there!!
I began adding up the numbers and discovered a pattern:
The pattern explained
with an equation is this:
10a + b + 10b + a
= 11a + 11b
= 11(a + b)
So for any number ab
ab + ba = 11(a + b)

6. And the mind still did not stop!!!
So I started looking at 3 digit numbers and saw the following pattern.
For any number abc
abc + bca + cab = 111(a + b + c)
The pattern explained:
100a + 10b + c + 100b + 10c + a + 100c + 10a + b
= 111a + 111b + 111c
= 111(a + b +c)

7. Let us test the pattern with a 3 digit number.
Have fun testing the patterns shown with other 2 digit and 3 digit numbers and
perhaps discover other patterns!

8. MATHS FUN WITH DIGIT SUMS
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