Tuesday, April 23, 2024

Kaprekar’s Sequence

by Mark Warner
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Ages: 5-11

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 number28
2) Reverse the digits82
3) Take the smaller number from the larger number82 – 28 = 54
4) Using this answer, go to step 2 and repeat the process a number of times54 – 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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