BrainBashers - Random Puzzles

Puzzle 413

I am compiling the BrainBashers world almanac and it now contains quite a few pages. But just how many?

I know that it takes 121 digits to print all of the page numbers in sequence.

So, how many numbered pages does the book have, and how many times does the number 9 appear?

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Puzzle 414

What comes next in this sequence:

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Puzzle 415

Alex can eat 27 chocolates in an hour, Billie can eat 2 chocolates in 10 minutes, and Charlie can eat 7 chocolates in 20 minutes.

How long will it take them to share and eat a large box of 120 chocolates while watching a movie?

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Puzzle 416

Last week I decided to cycle to my Grandparents's house.

On the 1^st day, I cycled half of the distance.

On the 2^nd day, I cycled one half of the remaining distance.

On the 3^rd day, I cycled three quarters of the remaining distance.

On the 4^th day, I cycled 10 miles.

On the 5^th day, I cycled two thirds of the remaining distance.

On the final day, I cycled the remaining 5 miles.

How far is it to my Grandparent's house?

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