The three problems below have a recurring mathematical theme. I'm not going to tell you what the theme is, though - that's up to you to discover!

Do email in solutions to just one or two of the problems if you can't solve them all.

One

Think of any three digit number, and repeat the digits to make a six digit number. For example, if you thought of 381, the six digit number is 381381.

I claim that every such six digit number is divisible by 91. Prove me right!

Two

My stamp collection consists of three books of stamps. Two tenths of my stamps are in the first book, several sevenths of my stamps are in the second book, and there are 303 stamps in the third book.

How many stamps are there in my collection? Is there just one solution to this problem?

Three

Captain Ahab's boat is several metres long.

Captain Ahab has both sons and daughters*.

Captain Ahab has more years than children, and is not yet 100 years old.

The product of Captain Ahab's age, of the number of children he has, and of the length of his boat in metres is 32118.

How old is he, how many children does he have, and how long is his boat?

*with apologies to literature, as this is untrue of his awesome character, Captain Ahab, the monomaniac protagonist of Herman Melville's Moby Dick.