Page 5 - CBQ-CL-6-CH-3 NUMBER PLAY

(ii) (c) 1331

(iii)(c) You may obtain a palindromic number.

(iv) To create a palindromic number, you can start with any number, reverse its digits, and then add
the reversed number to the original number. Repeating this process often leads to a palindromic
number. For example, starting with 56, reversing the digits gives 65. Adding 56 and 65 results in 121,
which is a palindrome.

10. (c) A is true, but R is false.

11. (a) Both A and R are true and R is the correct explanation of A.

12. Time now – 02:15
Now, the next palindromic time is 02:20
Hence, 02:20 – 02:15 = 5 minutes.
The next one after that is 03:30.
Hence, 03:30 – 02:20 = 70 minutes.

13. Case-I: Smallest 5-digit palindrome number (different digits) – 12321
Largest 5-digit palindrome number (different digits) – 98789
Sum = 12321 + 98789 = 111110
Difference = 98789 – 12321 = 86468

Case-II: Largest 5-digit palindrome (same digits) – 99999
Smallest 5-digit palindrome (same digits) – 11111

Sum = 99999 + 11111 = 111110
Difference = 99999 – 11111 = 88888

14. (a) Some numbers whose digits add up to 18 are:
99, 189, 288, 297, 369, 459, 567, 678, 777, 885, 993, 1098, 1187, 1276

(b) The smallest number whose digit sum is 18 = 99.

(c) The largest 5-digit number containing 0 whose digit sum is 18 = 99000.
The largest 5-digit number not containing 0 whose digit sum is 18 = 99900.

(d) A very big number having the digit sum 18 can be made.
Yes, we can make an even bigger number, e.g., 9999999999999999999999999999999... (with more

9s).

15.
As per Collatz Conjecture rule, starts with any number; if the number is even, take half of it; if the
number is odd, multiply it by 3 and add 1; and repeat till to reach 1.
The sequence formed with starting number 35 is as follows:
35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1

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