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Example 9: What is the sum of the smallest activity
and largest 4-digit palindromes? What is Colouring the Palindrome Chart
their difference? Write a number chart from 0-99 and colour the palindrome.
Numbers like 11, 22, ..., 99 are 0 step palindromes. In this
Solution: The largest 4-digit palindromic chart 0 step palindromes are coloured. If the number is 12
number = 9999 and its reverse is 21, then 12 + 21 = 33, which is a palindrome.
That means, starting from 12 or 21, we get a Palindrome in
The smallest 4-digit palindromic 1 step. Colour the numbers 12 and 21 red as shown below.
number = 1001 Colour the numbers in the table with different colours using
Sum = 9999 + 1001 = 11000 the colour code given below.
0 1 2 3 4 5 6 7 8 9
Difference = 8998 10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
Example 10: In a 12-hour clock, the time is 30 31 32 33 34 35 36 37 38 39
now 10:01. In how many minutes the clock 40 41 42 43 44 45 46 47 48 49
53
54
55
51
50
52
58
59
56
57
shows the next palindromic time? What 60 61 62 63 64 65 66 67 68 69
about the one after that? 70 71 72 73 74 75 76 77 78 78
80 81 82 83 84 85 86 87 88 89
Solution: In the 12-hour clock, the next 90 91 92 93 94 95 96 97 98 99
palindromic time after 10:01 is 11:11, which Colour Code
occurs after 70 minutes. After that, the next 1 step 2 steps 3 steps 4 steps 5 steps 6 steps
palindromic time will be 12:21.
Practice Time 3C
1. Take a number 2345. How many possible 4-digit numbers can you make by shifting the digits in it?
Write these numbers in tabular form. Can you colour the supercells or subcells in it?
2. Solve the puzzle:
I am a 4-digit number.
I am a Palindrome.
My tens digit is 3 more than my thousands digit.
The sum of my digits is 22.
What number am I?
3. Starting from some numbers we can get palindromes in 2 steps, 3 steps or 4 steps. Take an example
of each one that gives 2-step, 3-step and 4-step palindromes.
4. 10th February 2001 (10/02/2001) is a palindromic date. Find 10 such dates which are palindromic.
5. There are many palindromic decimals: 6.6, 31.13, 654.456, 9696.6969, ... . How many steps are required
to produce a palindromic decimal starting with 3.52?
6. Find three numbers less than 100 that require at least four steps to become palindromes.
7. There are many palindromic squares, such as 121, 484, etc. Can you find some more palindromic squares?
8. Palindromes which are multiples of 11 are 11, 22, 33, 44, 55, ... . What is the smallest multiple of 11
which is not palindromic?
85 Number Play
