Capicua or palindrome number is a number that can be read in either direction (right to left or left to right) and has exactly the same value, for example 6446.
To recognize a Capicua number, just look at it in both directions, left to right and right to left, and if the number doesn't change, it's considered a Capicua number.
Examples: 22, 171, 3993, 5555, 45854, 02022020, 9562659 and 741535147.
How to get a capicua number?
It is possible to create a capicua number from other numbers. To do this, follow these steps:
- Choose any number;
- Add the chosen number to its inverted value (inverted form of the number);
- Confirm that the result is a capicua number.
- If the number found is not capicua, just repeat the process until you find a new number. The calculation must be repeated until the capicua number is found in the result.
Examples of numbers that generate capicua:
Number 123:
123 + 321 = 444 (is a Capicua number).
Number 76:
76 + 67 = 143
143 + 341 = 484 (is a capicua number).
Number 68:
68 + 86 = 154
154 + 541 = 605
605 + 506 = 1111 (is a Capicua number).
Numbers that do not generate capicua (Lychrel numbers)
There are some numbers that do not generate a capicua, as is the case of 196 and 897. These numbers that do not create a capicua are considered a mystery in mathematics and are called Lychrel numbers.
Curiosities about the capicua numbers
1. All numbers formed by equal digits are also capicua. Examples:
- 11, 88, 222, 5555, 99999.
2. Any capicua number formed by an even number of digits is divisible by 11 and the result is an integer. Examples:
- 4664 ÷ 11 = 424
- 123321 ÷ 11 = 11211
- 2266 ÷ 11 = 206
- 5555 ÷ 11 = 505
- 244442 ÷ 11 = 22222
3. Numbers that are formed only by the digit 1 always generate a palindrome when multiplied by themselves. Examples:
- 11 x 11 = 121
- 111 x 111 = 12321
- 11111 x 11111= 123454321
- 1111111 x 1111111 = 1234567654321
4. Some dates also form capicua numbers. Examples:
- 02/22/2022 (the next Capicua date will be the last of the century)
- 02/02/2020 (last capicua date)
- 21/12/2112
- 8/10/2018
- 9/10/2019
- 30/03/3003
5. Any single digit number is a capicua:
- 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are capicua numbers.
