This
sequence is quite easy to work out, and it produces some interesting patterns.
Get the children to carry out the process, looking for patterns in their
work throughout.
| 1)
Think of a two-digit number |
28 |
| 2)
Reverse the digits |
82 |
| 3)
Take the smaller number from the larger number |
82
- 28 = 54 |
| 4)
Using this answer, goto step 2 and repeat the process a number
of times |
54
- 45 = 9
90 - 09 = 81
81 - 18 = 63... |
The
children should soon recognise the links with the nine times table. This
could then be used as a starting point for patterns within the nine times
table.
Ask
the children if there are any numbers for which Kaprekar's sequence does
not work (numbers with two digits which are the same - 11, 22, 33 etc.).
Why do they think this is the case?
Ask
them to test the sequence using three digit numbers. Does the same pattern
still result?
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