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 Post subject: NLCS 2011 paperPosted: Wed Feb 20, 2013 10:17 pm

Joined: Fri Feb 20, 2009 2:05 pm
Posts: 103
Jane is making spiral out of a wire.She bends the wire after 1cm, Then bends the wire after 2 cm, Then 3cm and continues in this manner.
After 4 bends She has used 15cm of wire.
How much wire will she have used after 6 bends?
How many bends will Jane have made when she uses 66cm of wire ?

Pls help ! I can't understand why is it 15 cm at he end of bend 4 , to begin with !

Queenma

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 Post subject: Re: NLCS 2011 paperPosted: Wed Feb 20, 2013 10:44 pm

Joined: Mon Aug 22, 2011 8:20 pm
Posts: 1706
Location: Warwickshire
With no bends you have 1 sides of your spiral - 1cm
After 1 bend you have 2 sides of your spiral - 1cm+2cm = 3cm
After 2 bend you have 3 sides of your spiral - 1cm+2cm+3cm = 6cm
and so on.
The number of sides of the spiral is always 1 more than the number of bends.
So 4 bends means 5 sides, therefore 1+2+3+4+5 = 15

Similary 6 bends means 7 sides, therefore 1+2+3+4+5+6+7 = 28

1+2+3+4+5+6+7+8+9+10+11 = 66
11 sides, 10 Bends

Formulaicly (where L is the lenght of wire and B is the number of bends) L = (B+1)(B+2)/2

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