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Palindromes Introduction to Palindromes Palindromic Sentences Palindromic Numbers Palindromic Dates Palindromic Times Palindromic Times and Dates A Palindrome Investigation

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Introducing Palindromes A palindrome is a word, a phrase, a sentence or a number that reads the same backwards as it does forwards. Here are a few palindromic words: madam kayak mum radar Can you find any more words that are palindromes?

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Palindromic Sentences Was it a cat I saw?

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Palindromic Sentences Too hot to hoot.

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Palindromic Sentences Sore eye Eros? No Miss, it is Simon.

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Palindromic Sentences Do geese see God?

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Palindromic Sentences Step on no pets.

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Palindromic Sentences Eva, can I stab bats in a cave?

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Palindromic Sentences Live not on evil!No evil I did, I live on.

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Palindromic Numbers Here are some numbers that read the same backwards as they do forwards: How many palindromes are there between 1 and 100?

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Find a Palindrome which is …. … a multiple of 3. … a multiple of 4. … a multiple of 5. … a multiple of 6. … a multiple of 7. … a multiple of 8. … a multiple of 9. … a multiple of 11. … a multiple of 12. Why do you think there are no palindromes which are multiples of 10?

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Find a Palindrome which is …. … a square number. … a triangular number. … a prime number.

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Find Two Palindromes …. … which have a difference of 2. … which have a difference of 10. … which have a palindromic difference. … which have a palindromic sum. … which have a palindromic product.

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Palindromic Dates What is special about 29th June 1992? It’s a palindrome! 29/6/92 Find as many palindromic dates as you can. When will the next palindromic date occur? When did the last palindromic date occur? What if you write the full year, not just the last two digits, for example 29/9/1992? What if you always use two digits for the month?

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Palindromic Times What is special about 9 minutes to 4 in the afternoon? It’s a palindrome! 15:51 How many palindromic times are there each day? List them all.

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Palindromic Times and Dates What is special about quarter to three on the afternoon of 5th April 1941? It’s a palindrome! 14:45 5/4/41 When will the next palindromic time and date occur? When was the last palindromic time and date?

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A Palindrome Investigation Choose any number. Reverse the digits and add to the number. Keep repeating this until you get a palindrome So 4075 produces a palindrome after just 1 addition. Continued...

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A Palindrome Investigation Choose any number. Reverse the digits and add to the number. Keep repeating this until you get a palindrome So 268 produces a palindrome after 2 additions Continued...

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A Palindrome Investigation Find starting numbers which produce palindromes after 1 addition, 2 additions, 3 additions, 4 additions, 5 additions, and so on. Are all of these possible? What is the largest number of additions that are needed to produce a palindrome? How many additions are required if you start with 89? How many additions are required if you start with 196?

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