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Sixty-seven Squared
Age 16 to 18
Challenge Level 
Why do this problem?
An excellent exercise in using geometric series with a fun way into the problem through experimenting with numbers and making conjectures.Possible approach
Let the students experiment with the numbers until they spot patterns and make conjectures. If they don't see how to prove the general result you may have to ask the 'key question' and suggest using the sum of a geometric series.Key questions
Can you write the number (k sixes followed by a 7) in terms of powers of 10 which will work for all k?Possible extension
Try the problem Clickety Click and All the SixesYou may also like
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