Liber Abaci/Problems

Problems from Liber Abaci by Leonardo Fibonacci

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?

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?

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?