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Additional Challenge

If you enjoy a little bit of an extra challenge then this page is for you. 

Why not see whether anyone else in your family wants to have a go too? 

Challenge 1

Palindrome 1

Meanings

Look up the meaning of ‘palindrome’ in a dictionary.

Words can be palindromic, for example ‘madam’.

Dates can be palindromic too, for example 17.8.71.

Can you think of some more examples?

Palindromic numbers

8, 33, 161, 222 and 2998992 are examples of palindromic numbers.

How many palindromic numbers are there between:

0 and 100? 100 and 200? 200 and 300? 300 and 400? 0 and 1000?

1000 and 1100? 1100 and 1200? 1300 and 1400?

 

Can you work out how many palindromic numbers there are between 0 and 2000?

What about between 0 and 10000?

 

Have fun and good luck!

Challenge 2

Palindrome 2 – you must complete ‘Palindrome 1’ before attempting this challenge

Backwards and forwards

Start with a two-digit number, for example: 32

Reverse it and add the result to the original number: 32 + 23 = 55

The result is palindromic after one reversal. 55

Now try it with another two-digit number, such as: 57

Reverse it and add the result to the original number: 57 + 75 = 132

Reverse and add again: 132 + 231 = 363

This time the result is palindromic after two reversals. 363

Can you find two-digit numbers that are palindromic after one reversal?

After two reversals? After three reversals? After more than three reversals?

The numbers 89 and 98 take 24 reversals!

Investigate the same process with three-digit numbers.

 

Have fun and good luck!

Challenge 3

Challenge 3 1
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