Palindromes

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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 stabbats 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
• 494 38283 145.541
• 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?
• Its 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?
• Its a palindrome!
• 1551
• 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?
• Its a palindrome!
• 1445 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.

4075
Reverse the digits and add to the number.
5704
9775
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.

268
Reverse the digits and add to the number.
862
1130
Keep repeating this until you get a palindrome.
311
So 268 produces a palindrome after 2 additions.
1441
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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END OF PRESENTATION