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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
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.
Q. Find the biggest number, less than 100, 
whose DIGIT SUM is 11? 
Let us now use each pair to get a possible answer.
We can see that 110 and 101 won’t work because their digit sums are 2 (1 + 1 + 0). 
Our answer is therefore 92.
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)
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)
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!
MATHS FUN WITH DIGIT SUMS 
brought to you by

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Maths Fun with Digit Sums

  • 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 brought to you by