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9. Here is a palindromic pyramid. Complete the pyramid.

11 × 11 = 121
111 × 111 = 12321

1111 × 1111 = 1234321

11111 × 11111 = 123454321
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10. Which two palindromic numbers less than 1000 have a difference of only 2?
11. What is the smallest number larger than 1000 that is palindromic?

12. Write the palindromic number less than 1000 which has a digit sum of 5?
13. Number 56665 is a palindrome. The next palindrome is 56765. If we say that 56665 is the first of
these palindromes, what will be the 8th palindrome?
14. Which 5-digit number is palindromic, has a sum of its digit equal to 27 and has a product of its digits
equal to 0?
15. Which three-digit number is palindromic, has a sum of its digits equal to 7 and has a product of its
digits equal to 12?
16. What is the sum and difference of the smallest and largest 5-digit palindromes?

17. Megha has a birthday on 12/02/2021, where the digits read the same from left to right and from right
to left. Find a few dates of this form from the past.

18. On the usual 12-hour clock, there are timings with different patterns 5:55, 10:01, and 12:21. Try and
find out some more possible times on a 12-hour clock of each of these types.
19. The product of two palindromes can also yield a palindrome.
11 × 22 = 242; 77 × 88 = 6776; ...
Can you find some other palindrome product yielding a palindrome? Check whether the statement
is true in all cases. If not, give an example where it fails.

Playing with Number Patterns

Swati and Vishnu were playing with number cards together. 2 2 2 4 2 2 2
Swati thought of a 3-digit number in her mind and asked Vishnu
to guess the number. When Vishnu asked her for some clues, 2 2 4 4 4 2 2
she showed him a pattern as shown in the given figure. Can you 2 4 2 4 2 4 2
guess the number now? 4 4 4 4 4 4 4
By looking at the pattern, we find that the digit 2 appears 28 times 2 4 2 4 2 4 2
and the digit 4 appears 21 times. 2 2 4 4 4 2 2
So, the number would be 2 × 28 + 4 × 21 = 56 + 84 = 140. 2 2 2 4 2 2 2

Here, we observe that a number can be arranged in some
patterns and figured out by using multiplication instead of repeated addition.

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