Page 60 - Maths Skill - 6

58 Maths

DIGIT SUM OF NUMBERS
According to this, the digit sum of a natural number in a given number base is the sum of all its digits.
For example, the digit sum of the decimal numbers 8072 would be
8 + 0 + 7 + 2 = 17
Besides this, there are many number of different number of digits, whose digit sum are same

i.e. 68, 176 and 545 have the same digit sum
here, 68 (a two digits number) = 6 + 8 = 14
176 (a three digits number) = 1 + 7 + 6 = 14

545 (a three digits number) = 5 + 4 + 5 = 14
Example : What is the largest 5 digit number whose digit sum is 14?
Solution : 95000 = 9 + 5 + 0 + 0 +0 = 14
Example : What is the smallest number whose digit sum is 14?
Solution : 59 = 5 + 9 = 14

PALINDROMIC NUMBERS
A palindromic number is a number that remains the same when its digits are reversed. In other words, it has
reflection symmetry across a vertical axis.
The term palindromic is derived from palindrome, which refers to a word were spelling is unchanged when its
letters are reversed.
Some palindromic numbers are 77, 878, 939, 4114, 6006, 111 and many more.

FORMATION OF PALINDROMIC NUMBERS

This method is applicable only when we start with the 2-digit number. All the two digit numbers with its reverse
and see what will be the result? If we get sum of palindromic number then stop otherwise we further add the result
with its reverse number.
Let’s see the given examples:

(i) 5 4 (ii) 2 9
+ 4 5 + 9 2
9 9 Palindromic number 1 2 1 Palindromic number

Challenge
I am a 4-digit palindrome.

(iii) 7 6 (iv) 9 6 I am an odd number.
+ 6 7 + 6 9 My ‘t’ digit is double of my
1 4 3 1 6 5 ‘u’ digit.
+ 3 4 1 + 5 6 1 My ‘h’ digit is double of my
4 8 4 Palindromic number 7 2 6 ‘t’ digit.
+ 6 2 7
1 3 5 3 Who am I? ___________
+ 3 5 3 1
4 8 8 4 Palindromic number

KAPREKAR CONSTANT
In 1949, D. R. Kaprekar discovered an interesting and magical phenomenon when playing with 4-digit numbers.