### Palindromes

A palindrome is a word, phrase, number or expression that reads the same backward as forward, e.g. Level, "Never odd or even", 12321 or

x + 22 = 22 + x

Here are some activities with a palindromic connection:

### Dates

3 — 2 — 23

4 — 2 — 24

5 — 2 — 25

6 — 2 — 26

7 — 2 — 27

8 — 2 — 28

9 — 2 — 29

Use long multiplication and pattern spotting to fill in the table with palindromic products.

Every whole number can be expressed as the sum of three palindromes.

How many steps does each number take to become palandromic?

How many palindromic numbers there are less than each power of 10.

Calculate the speed of the car from the palindromic odeometer readings.

Find calculations which written back to front give the same answer.

### Palindronic Primes

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What is the smallest palindromic prime number that is greater than 100?

### Palindromic Squares

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What is the largest palindromic square number that is less than 1000?

### Palindromic Cubes

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What is the smallest palindromic cube number that is greater than 1000?

### Roman Numerals

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What is the largest prime number that is palandromic when written in Roman numerals?

### Binary Palindromes

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Palindromic numbers are relatively rare in most number systems, but they appear more frequently in binary.

### Even Digits

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What is the only palindromic prime number that has an even number of digits?

Chris Smith, Twitter

Friday, February 3, 2023