Fibonacci plays the National Lottery

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Fibonacci plays the National Lottery

• An Investigation

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• Fibonacci plays the National Lottery.
• Last week I picked the following numbers on the
  National Lottery
• 1 , 4 , 5 , 9 ,
  14 , 23
• I did not win anything, so this week I picked the
  numbers
• 2 , 5 , 7 , 12 , 19 , 31
• Again I did not win anything so next week I will
  try another sequence in which each number, after
  the first two numbers have been selected, is the
  sum of the two previous numbers. i.e. a
  Fibonacci sequence.
• How many different possible Fibonacci sequences
  are there that you can pick in the lottery?

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• Solution
• Starting with a and b then the terms of the
  sequence are
• a , b , ab , a 2b , 2a 3b , 3a 5b
• To have the numbers on a lottery ticket we would
  need
• altb
• and
• 3a 5b 49
• The table shows the possibilities

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• There are therefore 23
• possible Fibonacci sequences possible in the
  National Lottery.
• Has a Fibonacci sequence ever won
• the jackpot in the National lottery?
• No, not yet.