Page 59 - Revised Maths Wisdom Class - 6

Number Play 57

If we talk about the three digit numbers, that are

100, 101, 102 _________ 999
here, the biggest three digit number = 999
and the smallest three digit number = 100
then total three digits number = 999 – 100 + 1 = 900

If we talk about the four digits number, that are
1000, 1001, 1002 _________ 9999

here, the biggest four digit number = 9999
and the smallest number = 1000
then total four digits numbers = 9999 – 1000 + 1 = 9000
If we talk about the five digit numbers, that are

10000, 10001 _________ 99999
here, the biggest five digit number = 99999
and the smallest five digit number = 10000

then, total five digits number = 99999 – 10000 + 1 = 90000
Now the formula governs the above concept
Total ‘x’ digits number = Biggest number of ‘x’ digit – smallest number of ‘x’ digit + 1

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 1: What is the largest 5 digit number whose digit sum is 14?

Solution: 95000 = 9 + 5 + 0 + 0 +0 = 14

Example 1: 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.