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Look at the sequence below:
$1, 2, 4, 8, 16...$
Can you describe how to get from one term to the next?
Can you describe the $n^{th}$ term of the sequence?
Now try adding together terms from the sequence:
$1 + 2$
$1 + 2 + 4$
$1 + 2 + 4 + 8$
Do you notice anything interesting?
Can you predict what $1 + 2 + 4 + ... + 64 + 128$ would be? Check to see if you are right.
How could you write the answer to $1 + 2 + 4 + ... + 2^n$?
Justify why your formula works.
Hint for building block B: Think about moving all the discs except the largest one onto the middle peg first.
Hint for Extension question: Current theory and observations suggest that between 13.5 and 14 billion years have elapsed since the Big Bang.
Tower of Hanoi
Age 11 to 14
Challenge Level 
Look at the sequence below:
$1, 2, 4, 8, 16...$
Can you describe how to get from one term to the next?
Can you describe the $n^{th}$ term of the sequence?
Now try adding together terms from the sequence:
$1 + 2$
$1 + 2 + 4$
$1 + 2 + 4 + 8$
Do you notice anything interesting?
Can you predict what $1 + 2 + 4 + ... + 64 + 128$ would be? Check to see if you are right.
How could you write the answer to $1 + 2 + 4 + ... + 2^n$?
Justify why your formula works.
Hint for building block B: Think about moving all the discs except the largest one onto the middle peg first.
Hint for Extension question: Current theory and observations suggest that between 13.5 and 14 billion years have elapsed since the Big Bang.
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