MATHS WEEK 2020 was a huge success with thousands of our readers enjoying taking part with our daily puzzles. It’s not too let, if you want to catch up - give them a go!

Sunday’s puzzle: The Answer 

466 rabbits

The Method:

At start of month 1, we have two rabbits. Number of pairs: 1

At end of month 1, they are ready to mate. Number of pairs: 1

At end of month 2, they have two babies. Number of pairs: 2

At the end of month 3, they have another pair, the first babies mate. Number of pairs: 3

At end of month 4, they have two more babies, the first pair have a pair and the second pair mate. Number of pairs: 5

At the end of month 5, they have another pair; their first pair have another pair. Their second pair have a pair. That is three more pairs. That is 8 pairs.

Now, we could go on for 12 months. We could do out a table, which is another good approach in problem solving.

However, you may notice already a pattern emerging in the numbers above. At each month, the total number of pairs is the sum of the totals for the previous two months.

1 + 1 = 2; 2+ 1 = 3; 3+2 = 5; 5+3 = 8; and so on.

Now that we see the pattern, we can extend the series on without drawing a table:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584…

The 12th term in the series is 144.

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That is how many pairs of rabbits will be in the field at month 12.

And, there would be 233 pairs at the end of the 12th month.

You may have seen this series before; it is now named the Fibonacci Series and comes up in the most surprising places in maths.

This is a mathematical model that can help us predict what will happen in the future, given a starting condition and rules. Even if the mathematical equations are good and tested well, the outputs from such a model should be carefully interpreted.

For instance, the Fibonacci model makes a lot of assumptions that do not reflect the real world. That is why mathematical models must be used with good science. Such models are often tested against real world data to see if they are useful. Usually they will be added to and modified as more knowledge becomes available.

This is the case with the complex models used in understanding the Covid pandemic.

All puzzles are by Eoin Gill, the coordinator of Maths Week Ireland and director Calmast STEM Engagement Centre, Waterford Institute of Technology