City of London question
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City of London question
This is from a 10+ paper. Can anyone help me explain to a 9 year old without the formula 2^n -1. No calculator is allowed. Is there a quick way to get to the 50th student?
The number 1 is written on a piece of paper and then passed round the
room to each of 50 students in turn. Each student must cross out the
number seen and replace it with its double plus 1.
b. The last student does this then announces the final number.
What should the final number be?
The number 1 is written on a piece of paper and then passed round the
room to each of 50 students in turn. Each student must cross out the
number seen and replace it with its double plus 1.
b. The last student does this then announces the final number.
What should the final number be?
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- Joined: Sun Nov 30, 2008 7:38 pm
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This threw me to start with... the only easy technique is to change it to binary!
Then each pass of the card results in a left shift (a double in base 2) and a 1 being added on the right
i.e.
initial 1
next 11
next 111
next 1111
which as said above leads to.... 2^n-1
Tricky question... assume a filler to see what people write.
Regards
SVE
Then each pass of the card results in a left shift (a double in base 2) and a 1 being added on the right
i.e.
initial 1
next 11
next 111
next 1111
which as said above leads to.... 2^n-1
Tricky question... assume a filler to see what people write.
Regards
SVE
Animis opibusque parati