Maths Fun with Digit Sums
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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 of12345 = 1 + 2 + 3 + 4 + 5 = 15
![Page 2: Maths Fun with Digit Sums](https://reader033.fdocuments.us/reader033/viewer/2022061214/549a6312b4795922438b4606/html5/thumbnails/2.jpg)
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.
1 + 102 + 93 + 84 + 75 + 6
10 + 1 9 + 2 8 + 3 7 + 4 6 + 5
![Page 3: Maths Fun with Digit Sums](https://reader033.fdocuments.us/reader033/viewer/2022061214/549a6312b4795922438b4606/html5/thumbnails/3.jpg)
Q. Find the biggest number, less than 100, whose DIGIT SUM is 11?
Let us now use each pair to get a possible answer.
1 + 102 + 93 + 84 + 75 + 6
10 + 1 9 + 2 8 + 3 7 + 4 6 + 5
11029384756
101 92 83 74 65
![Page 4: Maths Fun with Digit Sums](https://reader033.fdocuments.us/reader033/viewer/2022061214/549a6312b4795922438b4606/html5/thumbnails/4.jpg)
We can see that 110 and 101 won’t work because their digit sums are 2 (1 + 1 +
0).
Our answer is therefore 92.
1 + 102 + 93 + 84 + 75 + 6
10 + 1 9 + 2 8 + 3 7 + 4 6 + 5
11029384756
101 92 83 74 65
![Page 5: Maths Fun with Digit Sums](https://reader033.fdocuments.us/reader033/viewer/2022061214/549a6312b4795922438b4606/html5/thumbnails/5.jpg)
But my mind would not stop there!!I began adding up the numbers and
discovered a pattern:
29 + 92 = 12138 + 83 = 12147 + 74 = 12156 + 65 = 121
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)
![Page 6: Maths Fun with Digit Sums](https://reader033.fdocuments.us/reader033/viewer/2022061214/549a6312b4795922438b4606/html5/thumbnails/6.jpg)
And the mind still did not stop!!!So I started looking at 3 digit numbers
and saw the following pattern.
For any number abcabc + 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)
![Page 7: Maths Fun with Digit Sums](https://reader033.fdocuments.us/reader033/viewer/2022061214/549a6312b4795922438b4606/html5/thumbnails/7.jpg)
An example:562 + 625 + 256 = 1443
The Digit Sum of 562 is 5 + 6 + 2 = 13111 x 13 = 1443
Proving that 562 + 625 + 256 = 111(5 + 6 + 2)
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!
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