Chapters 5-6: The Multiplying Gremlins

 Would you believe that the problem of the multiplying gremlins is more than eight hundred years old? Its original version (which used pairs of rabbits instead of gremlins) appeared in Liber abbaci ("The Book of Calculation"), which was published in 1202 by Leonardo Pisano Fibonacci (c. 1170-c. 1250). Liber abbaci was the book that introduced the decimal system and Hindu-Arabic numerals (1, 2, 3, etc. - the ones you and I all know) to Europe. Before then, Europeans were still counting on their fingers or using Roman numerals and large tables called "abacus boards," on which people moved counters back and forth to make calculations.  An ancient page from Liber abbaci Leonardo Pisano Fibonacci

"The Rabbit Problem," as it has come to be known, is the most famous problem from Liber abbaci, but there are many others. Several hundred pages, in fact, all written and copied by hand, since the printing press hadn't been invented yet. The sequence of numbers that form the answer to the problem - 1, 1, 2, 3, 5, 8, 13, etc. - is now known as the Fibonacci Sequence. And amazingly, you can find the numbers in the Fibonacci Sequence all throughout nature!
Here's another problem from Liber abbaci. A "denaro" (plural "denari") was a unit of money used in Fibonacci's time.
 "A certain man buys thirty birds which are partridges, pigeons and sparrows, for thirty denari. A partridge he buys for three denari, a pigeon for two denari, and two sparrows for one denaro, namely one sparrow for one-half denaro. It is sought how many birds he buys of each kind."
Hint - At first glance, it looks like there's not enough information to solve this problem. Remember, though, that the man buys more than zero of each bird, and he can't buy a fraction of a bird.
Click below to see how I worked it out.
Did you get the same answer?
Numbers in the Fibonacci Sequence appear all over nature! Click on the links below to see some examples:

Nature, The Golden Ratio, and Fibonacci too ...
How are Fibonacci numbers expressed in nature?
How to draw a "Fibonacci Spiral" 