Fibonacci plays the National Lottery

An Investigation

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?

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

a

b

2 3 4 5 6 7 8 9

1 2 3 4 5

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.