The Background
The cache is not at the solution of the puzzle below, as that would be too easy! In the book the hero and heroine have some inside information, which means only they can solve it. You quite rightly aren't allowed to publish a cache that people can't solve, so I've had to modify it slightly to make it work here. You need to solve the puzzle below, and then find the source of the extra information required to take you to the final location.
Fibonacci numbers
The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits, one male, one female, is put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was... How many pairs will there be in one year?
OK, now the good news - the answer is a very famous series. The number of pairs of rabbits at the end of each month is 1,1,2,3,5,8,13,21,34,55,89,144 etc. If you haven't come across them before, each number is the sum of the previous two.
These are known as the Fibonacci numbers, and they have some fascinating properties.
- Try dividing each one by the previous one. start from the left and work to the right. Are you beginning to home in on a number?
- Try dividing each one by the following one and adding one - same number?
- Get a calculator. Type in 1. Add 1. Do 1/x (the reciprocal). Add 1. 1/x. Add 1. 1/x. Keep repeating. What number do you get?
- Calculator again - type in 1 add 1. Take the square root. Add 1. Square root. Add 1. Square root. Keep repeating. What number do you get?
Write the number down as A.BCDEFGH (don't forget to round if necessary).
North is 51 AB.(CDE+FGH). West is another matter.
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