Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat this for a number of your choice from the second row. You
should now have just one number left on the bottom row, circle it.
Find the total for the three numbers circled. Compare this total
with the number in the centre of the square. What do you find? Can
you explain why this happens?
Can you go through this maze so that the numbers you pass add to
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
I was in Bewdley, in Worcestershire recently. It's a very old
town and well known for a pretty bridge over the river in the
centre of town. But it's also known for another reason, one that
most people don't know about. Mr Edward Benbow, from Bewdley, holds
the palindromic record! "The what?" you may be asking.
A palindrome is a word, sentence or verse that reads the same
forward or backwards, that is to say from right to left and left to
right. EVE and ANNA are both short palindromic names, then there's
HANNAH and BOB. You probably have some palindromic people in your
family! Not sure? Well how about MUM or DAD, and you might even
have a SIS!
Was it a car or a cat I saw? The letters need a little
adjusting, but that is a palindromic sentence, or rather
Mr Benbow has put together 22,500 words to make a "palindromic
composition"! They don't make a great deal of sense but that's a
lot of words to read backwards.
Numbers can also be palindromes. For instance 121, this can be
read backwards or
forwards. Palindromic numbers are very easy to create from other
numbers with the aid of addition.
1. Write down any number that is more than one digit. (e.g.
2. Write down the number reversed beneath the first number.
3. Add the two numbers together. (121)
4. And 121 is indeed a palindrome.
Try a simple one first, such as 18.
Sometimes you need to use the first addition answer and repeat
process of reversing and adding.
You will nearly always arrive at a palindrome answer within six
steps. Try one of these numbers 68 or 79.
If you choose a number greater than 89 arriving at the
palindrome answer takes more steps but it still works.
But don't try 196! In fact, avoid it like the plague.... A
computer has already gone through several thousand stages and still
hasn't come up with a palindrome answer!
I wonder if you can think how many 2 digit palindromes there
are? How about finding all of the 3, 4, 5 or 6 digit ones? How
about to a million digits! Some people have already beaten you to
that, you'll be glad to know. You can find the results of their
work on the web here
Don't get palindromes mixed up with inversions . Inversions describe
numbers that read the same upside down as the right way up. Look at
Can you think which year in the last century read the same when
inverted? How about a year in the century before last? When will
the next one occur?
So how and where did the idea of Palindromes come from? Well we
know a great deal more about word palindromes. The word itself is
from the Greek palindromus , which means to run back again. The
palindromes that were made up by organising groups of words not
letters. A Greek poet, Sotades , who
lived in Egypt in about 276BC during the reign of Ptolemy II, wrote
a palindrome about the king which wasn't appreciated. Poor old
Sotades was sealed in a box and cast out to sea for his efforts.
Palindromes are found written in Egyptian hieroglyphics and in
Latin texts. Despite quite a search, I have not been able to
uncover anything significant about the history of the number
palindrome. There is a journal written especially for people who
are passionate about palindromes and there are many, many
palindrome web sites. Some provide information on the findings of
who investigate how they can be formed and the patterns found when
they create palindromes. Other sites provide palindrome puzzles and
problems for you to solve. Maybe you can become the new Harvey
Duner who, from July 18th 2001, became a record breaker with a
palindrome prime of 39,027 digits. What can we say Harvey, except
it could have been 39,093 digits!