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Hint: It didn't matter how many male or female borrowers there were.

Answer: 4200 books.

It doesn't matter how many female borrowers there were as 1/2 of the females accepted the books, and those that did accepted 6 books, which is 3 books per female on average.

Similarly it doesn't matter how many male borrowers there were as 3/4 of the males accepted 4 books each, which is again 3 books each.

So both the males and females accepted, on average, 3 books each. And 1400 * 3 = 4200. QED.

Puzzle 2

At dawn on Monday a snail fell into a bucket that was 12 inches deep.

During the day it climbed up 3 inches, however, during the night it fell back 2 inches.

On what day did the snail finally manage to climb out of the bucket?

[Ref: ZQGM]

Hint: The answer isn't 12 days.

Answer: The following Wednesday, nine days later.

At dawn on Monday the snail was at the bottom. Each day it climbed 3 inches, and dropped 2 inches over night, so at the start of the next day it was 1 inch higher, so:

Hint: How many chickens did the last customer buy?

Answer: 15 chickens.

The first customer bought 15 ÷ 2 + ½ = 8 (leaving 7)
The second customer bought 7 ÷ 2 + ½ = 4 (leaving 3)
The first customer bought 3 ÷ 2 + ½ = 2 (leaving 1)
The first customer bought 1 ÷ 2 + ½ = 1

The answer can be worked out in the following way:

The fourth customer can only have bought one chicken, otherwise there would be some chickens left. The third customer bought all but 1, so total - (total ÷ 2 + ½) = 1. This can be solved algebraically or it's easy to see that the total must have been 3. This method keeps working until we reach the first customer.

Puzzle 4

I am compiling the new BrainBashers world almanac and it now contains lots more pages.

I know that it takes 333 digits to print the page numbers in sequence.

How many numbered pages does the book have and how many times does the number 3 appear?

Hint: Think of the pages from 1-9, and then 10-99.

Answer: There are 147 pages and the number 3 appears 35 times.

Stage 1
=======
For pages 1 - 9 we have a total of 9 digits. For pages 10 - 99 we have a total of 180 digits. This is a total so far of 189, therefore we require another 144 digits, which is another 48 pages. Taking us to 147 pages in total.

Stage 2
=======
From page 1 to 147 we have 15 times where the page number ends in 3. We also have the ten pages in the 30's, and the ten pages in the 130's that have the extra 3 in them. For a total of 35 number 3s.

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