Fruit-ful Puzzler

Three crates wash up on your tropical beach. Each crate is labelled. The labels read “apples”, “oranges”, “apples and oranges”. You know the labels are all mixed up and none of them is on the right crate. Reach into one crate, pull out a single piece of fruit and you will know how to label the crates correctly.  Which crate do you choose?

Pick any numbered dot to begin. You must place a coin on an empty dot and slide it across the diagram to another empty dot. Once a dot is filled, you may not use it again, and only one slide per coin placed! Example: Drop coin on #6, you may slide to either #3 or #1.  Can you fill 7 dots and drop your final coin on the remaining one? It is not as easy as it seems!

Three crates wash up on your tropical beach. Each crate is labelled. The labels read “apples”, “oranges”, “apples and oranges”. You know the labels are all mixed up and none of them is on the right crate. Reach into one crate, pull out a single piece of fruit and you will know how to label the crates correctly.  Which crate do you choose?

You must reach into the crate labelled “apples and oranges”. If you pull out an apple, then you know this is the apples crate. This then means that the one labelled “oranges” cannot be either “apples” or “oranges”, since all the labels are incorrect, so it must be the “apples and oranges” crate.  That makes the crate labelled “apples” actually the “oranges”.
If you pull out an orange, then this is the “oranges” crate, and the “apples” crate must actually be “apples and oranges”, so the “oranges” crate would be “apples”.

Pick any numbered dot to begin. You will need 8 coins. You must place a coin on an empty dot and slide it across the diagram to another empty dot. Once a dot is filled, you may not use it again, and only one slide per coin placed! Example: Drop coin on #6, you may slide to either #3 or #1.  Can you fill 7 dots and drop your final coin on the remaining one? It is not as easy as it seems!

The logic here is to slide your coin to fill the dots as though you were following one continuous line on the diagram.  Pretend you are tracing the diagram with a pencil without lifting it. You would begin at 1, move to 4, 7, 2, 5, 8, 3, 6.  You can begin at any number, but then fill the dots in order by attached lines.

Take your first coin. Place it on dot 6 or 4 so that you can slide it to 1.
Now 1 is filled, so to fill 4, you must place your coin on 7 and slide it.
To fill 7, you place a coin on 2 and slide it.
To fill 2, you place a coin on 5 and slide it.
To fill 5, you place a coin on 8 and slide it.
To fill 8, you place a coin on 3 and slide it.
To fill 3, you place a coin on 6 and slide it.
6 is the only remaining open dot, so place your final coin on 6.

The key word in the clue is ten.  The only way to get a number from letters is to think of Roman Numerals, so the result is:
Animal Word: Fox
Drop First Letter to create another animal word: Ox
Drop First Letter to find ten: X (Roman Numeral for 10)