Liber Abaci/Problems
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Problems from Liber Abaci by Leonardo Fibonacci
The Lion, the Leopard and the Bear
- A lion would take $4$ hours to eat $1$ sheep.
- A leopard would take $5$ hours.
- A bear would take $6$.
- If a single sheep were to be thrown to them, how many hours would it take to devour it?
Bezants and a Seventh
- A man left to his oldest son $1$ bezant and a seventh of what was left;
- then, from the remainder, to his next son he left $2$ bezants and a seventh of what was left;
- then, from the new remainder, to his third son he left $3$ bezants and a seventh of what was left.
- He continued in this way, giving each son $1$ bezant more than the previous son and a seventh of what remained.
- By this division it developed that the last son received all that was left, and all the sons shared equally.
- How many sons were there and how large was the man's estate?
Orchard with Seven Gates
- A man entered an orchard with $7$ gates, and there took a certain number of apples.
- When he left the orchard he gave the first guard $\dfrac 1 2$ the apples and $1$ apple more.
- To the second guard he gave $\dfrac 1 2$ of his remaining apples and $1$ apple more.
- He did the same for all the remaining $5$ guards, and left the orchard with $1$ apple.
- How many apples did he gather in the orchard?