Palindromes in mathematics are ubiquitous. For one, all the single digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are technically palindromes – they do look the same no matter which "side" you consider them from. They are just a drop in the sea of interesting examples that showcase the beauty of numbers and the relationships between them.
It’s important to note that palindromic numbers can be seen in practically any numerical system one can think of. It’s not necessary to venture outside most people’s comfort zone of the decimal system to find fascinating instances, though. An excellent example of palindromes occurring in mathematics is the case of perfect powers.
There exist countless palindromic perfect powers nk, where:
- n is a natural number (n∈N); and
- k=2, k=3 or k=4.
Examples of such palindromic squares include 121, 484, 676, 10201, 12321, 14641; palindromic perfect cubes are, among others, 1331, 1030301, 1367631; and you can even find palindromic fourth powers such as 14641, 10406040 or 1004006004001.
You don’t have to wander into the realm of powers to find palindromic numbers, though. In fact, there’s quite a lot to come across if you simply enumerate… As we’ve already established, in the decimal system, there are exactly ten single-digit palindromes, but on top of that, we have:
- 9 palindromic numbers with two digits (11, 22, 33, 44, 55, 66, 77, 88, 99),
- 90 palindromic numbers with three digits (for example 101, 111, 121, and so on to 999), and
- 90 palindromic numbers with four digits (1001, 1111, 1221, …, 9779, 9889, 9999).
💡 Did you know you can create palindromes from non-palindromic numbers? The operation is known as the Lychrel process, and it works by "reversing" the digits of any number and then adding them. After doing it several times, you will get a palindrome at some point! Let's go through an example, starting with the number 273.
- 273 → 372
- 273 + 372 = 645
- 645 → 546
- 645 + 546 = 1191
- 1191 → 1911
- 1191 + 1911 = 3102
- 3102 → 2013
- 3102 + 2013 = 5115
And voila! Using the Lychrel procedure, we easily arrived at the palindromic number 5115 starting from a non-palindrome.
FAQs
According to Aziz Inan, University of Portland's professor of engineering, "Eight-digit palindrome dates are very rare and are clustered in the first three or so centuries at the beginning of a millennial, and then don't show up for 600 to 700 years, until they appear as a cluster in the next millennium".
How to calculate palindrome date? ›
Approach: Since the first four digits (i.e. the day and the month) have to be the reverse of the last four digits (the year) in order for the date to be a palindrome. So, every year will have at most one palindrome date.
Is a palindrome date lucky? ›
The final palindrome date of the 21st century using this format will occur in 2092 on leap day, 29 February (29-02-2092). The Farmers' Almanac also said palindrome dates are supposed to be lucky because they are considered rare.
Is 4 2 24 a palindrome date? ›
Since the U.S. uses the mm/dd/yyyy format, palindromes are more frequent in the United States, than in other parts of the world. April palindrome dates include: April 2, 2024 (4-2-24) April 20, 2024 (4-20-24)
How many 7-digit palindromes are there? ›
Therefore, there are: 9 * 10 * 10 * 10 * 1 * 1 * 1 = 9,000 7-digit palindromes.
What is the next palindrome date in 2024? ›
It started on Saturday April 20th 2024 (4-20-24) and will end on April 29th 2024 (4/29/24). LIST OF PALINDROME DAYS IN 2024: April 2, 2024 (4-2-24) April 20, 2024 (4-20-24)
How many palindrome dates are there in 2025? ›
There will be 11 palindrome dates every year from 2025 to 2029 under the m/dd/yy format, according to Farmers' Almanac.
How many palindromes are there in April 2024? ›
This month features eleven dates that are the same backwards as forwards. The first palindrome date was the four-digit form of April 2nd; 4/2/24. April 20th is the only seven-digit palindrome of the month; 4/20/2024. The 20th also kicks off a stretch of ten consecutive palindrome days.
How do you solve a palindrome problem? ›
Solution 1: Convert to String and Reverse
- Step 1: Convert the given integer to a string to make it easier to reverse.
- Step 2: Reverse the string using Java's StringBuilder class.
- Step 3: Compare the original and reversed strings. If they are equal, the number is a palindrome.
| Twosday |
|---|
| Significance | Palindromic and ambigramic Gregorian calendar date marked by exclusivity or prevalence of digit 2; fad |
| Celebrations | Mass weddings, time capsules, sales promotions |
| Date | February 22, 2022 |
| Frequency | Every 400 years |
1 more rowAccording to the Farmer's Almanac, the next 5 years will all contain consecutive palindrome dates, shifting one month every year. According to timeanddate.com, the current millennium will feature 36 palindrome days, the first occurring on October 1, 2001, and the last will occur on September 22, 2290.
What is an angel date? ›
angel date (plural angel dates) (euphemistic) The anniversary of the death of a child.
What is the palindrome date in 2027? ›
Is 3 22 23 a palindrome date? ›
It's not a palindrome, which is a word or number sequence that can be read the same way forward and backward. There was a 10-day stretch of palindromes back in March of this year: 3-20-23, 3-21-23, 3-22-23, 3-23-23, 3-24-23, 3-25-23, 3-26-23, 3-27-23, 3-28-23 and 3-29-23.
Is 2 22 22 a palindrome date? ›
Feb. 22, 2022, is written out numerically is 2/22/22. Not only is it a palindrome because it reads the same forward and backward, but what makes it special is the date has all twos.
How many 8 digit palindromes are there? ›
Then the fifth digit is the same as the third, the sixth is the same as the second, and the last is the same as the first, so there are 9000 7-digit palindromic numbers; There are also 9000 palidromic 8-digit numbers, since, the only difference is that the fifth digit is the same as the forth, the sixth is the same as ...
How rare are palindrome birthdays? ›
Some Palindrome Dates are Rare
Depending on date formats, palindromic dates can be rare. Aziz S. Inan, an electrical engineering professor at the University of Portland, has calculated that in the mm-dd-yyyy format, Palindrome Days tend to occur only in the first few centuries of each millennium (1000 years).
What is the palindrome date for 2026? ›
May 20, 2025 (5202025) 20. June 20, 2026 (6202026) 21. July 20, 2027 (7202027) 22.
What is the smallest 8 digit palindrome number? ›
To find the smallest such number, we need to assign the smallest possible values to A and B. Let's assign A = 1 and B = 0. Therefore, the smallest eight-digit palindrome number with only two different digits is 10000001.
