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# Palindromic Numbers Trivia Quiz

### Let see how much do you know about these intriguing palindromic numbers in the world of mathematics. Enjoy and have fun!

A multiple-choice quiz by Matthew_07. Estimated time: 5 mins.

Author
Time
5 mins
Type
Multiple Choice
Quiz #
287,831
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
2870
Awards
Top 20% Quiz
Last 3 plays: Guest 110 (0/10), Guest 180 (8/10), panagos (10/10).
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Question 1 of 10
1. Palindromic numbers are numbers that read the same from left to right and from right to left. In other words, they are "symmetrical" numbers. Which of the following mathematical products does NOT yield a palindromic number? Hint

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Question 2 of 10
2. Notice that the year 2002 is a palindrome. So, what will be the next palindromic year?

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Question 3 of 10
3. Palindromic primes are numbers that are both palindromic and prime. Which of the following numbers is the greatest 3-digit palindromic prime? Hint

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Question 4 of 10
4. The first 5 palindromic primes are 2, 3, 5, 7 and 11. Actually, these numbers are also the first 5 prime numbers. What is the next palindromic prime in the series? Hint

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Question 5 of 10
5. Palindromic squares are numbers that are simultaneously palindromic and square. For example, 111 x 111 = 12321. Notice that 111111111^2 (nine 1's) = 12345678987654321. So, is 1111111111^2 (ten 1's) still a palindromic square?

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Question 6 of 10
6. The first 3 palindromic squares are 1, 4 and 9. What number comes next?

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Question 7 of 10
7. Choose the WRONG statement. Hint

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Question 8 of 10
8. Denote a palindromic number (of any digits) as X. Now, reverse the number to get Y. Will the difference between X and Y always be 0?

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Question 9 of 10
9. You find a lock on an ancient chest. The password is a 4-digit palindromic number, using the digits from 0 to 9, and you are given that the first digit of the password is 9. You need at most ___ attempts to open the chest. Hint

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Question 10 of 10
10. A car meter currently reads 12345. What palindromic number will next appear on it?

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Quiz Answer Key and Fun Facts
1. Palindromic numbers are numbers that read the same from left to right and from right to left. In other words, they are "symmetrical" numbers. Which of the following mathematical products does NOT yield a palindromic number?

Answer: 131 x 131 = 17161

Notice the following patterns:
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
You can continue this until 111111111 x 111111111 = 12345678987654321.
2. Notice that the year 2002 is a palindrome. So, what will be the next palindromic year?

Other examples of palindromic years are 2222, 2332 and 2442. A very interesting fact that I found online is that there exists a Universal Day Of Symmetry. For example, at 10.01am on 10 January 1001, the time can be written as 100110011001. Another one would be at 20.02pm on 20 February 2002, which can be written as 200220022002. Both of these are palindromic numbers, and these are the only 2 cases, since it is impossible for us to have 300330033003 based on the 24 hour clock system.
3. Palindromic primes are numbers that are both palindromic and prime. Which of the following numbers is the greatest 3-digit palindromic prime?

Notice that 999 and 939 are not prime numbers, since they can be divided by 3. A very simple way to determine whether a number can be divided by 3 is to sum up all the individual digits in that number. If the sum can be divided by 3 then so can the number itself. For example, the sum of all the individual digits of 999 is 9 + 9 + 9 = 27. 27 is divisible by 3.

Both 929 and 919 are prime numbers, but 929 is greater than 919, so 929 is the answer.
4. The first 5 palindromic primes are 2, 3, 5, 7 and 11. Actually, these numbers are also the first 5 prime numbers. What is the next palindromic prime in the series?

22, 33, ..., 99 are all divisible by 11 so they are not palindromic primes.
5. Palindromic squares are numbers that are simultaneously palindromic and square. For example, 111 x 111 = 12321. Notice that 111111111^2 (nine 1's) = 12345678987654321. So, is 1111111111^2 (ten 1's) still a palindromic square?

The series stops at 1111111111^2 (ten 1's), where the product is 1234567900987654321, which is NOT a palindromic number, although it is indeed a square.
6. The first 3 palindromic squares are 1, 4 and 9. What number comes next?

A longer list is:
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
11 x 11 = 121
22 x 22 = 484
26 x 26 = 676
and so on.
7. Choose the WRONG statement.

Answer: The sum of 2 palindromic numbers must NOT be a palindromic number.

The sum of 111 and 111 is 222, which is still a palindromic number. All numbers from 1 until 9 are palindromic. Therefore, 10 is the smallest non-palindromic number. 22, 33, ..., 99 are all divisible by 11. Hence, they are not palindromic primes.
8. Denote a palindromic number (of any digits) as X. Now, reverse the number to get Y. Will the difference between X and Y always be 0?

From the definition, if X is palindromic, then its reverse, Y has the same value. Therefore, X = Y and hence X - Y = 0.
9. You find a lock on an ancient chest. The password is a 4-digit palindromic number, using the digits from 0 to 9, and you are given that the first digit of the password is 9. You need at most ___ attempts to open the chest.

The password is in the form of 9XX9. So, the possible passwords are 9009, 9119, 9229, ..., 9999.

According to Patrick De Geese, the only palindromic cube whose cube is not palindromic is 10662526601, where its cube root is 2201, or 2201^3 = 1066256601.
10. A car meter currently reads 12345. What palindromic number will next appear on it?

It is certainly not 12321. Any number in the form of 123XX should not be right. So, we try to find numbers in the form of 124XX. So, the next palindromic number is 12421.
Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
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This quiz is part of series Fun with Numbers:

A collection of my mathematics quizzes, covering different types of numbers with interesting properties. This list includes composite numbers, consecutive numbers, Fibonacci numbers, palindromic numbers, perfect numbers, prime numbers, square numbers, and triangular numbers.

1. Composite Numbers Average
2. Consecutive Numbers Average
3. Fibonacci Numbers Average
4. Palindromic Numbers Average
5. Perfect Numbers Average
6. Prime Numbers Tough
7. Square Numbers Average
8. Triangular Numbers Average