2. Fibonacci plays the National Lottery An Investigation

3. 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?

4. Solution Starting with ‘a’ and ‘b’ then the terms of the sequence are a, b, a+b, a + 2b, 2a + 3b, 3a + 5b To have the numbers on a lottery ticket we would need a<b and 3a + 5b 49 The table shows the possibilities

5. a b 23456789 1  2  3  4  5 

6. 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.