Medium Puzzles 

Workings

Hint
As we don't know how of the people were library members, you can try a random number and see what happens.

Answer
4,200 books.

Reasoning
It doesn't matter how many library members there were, as ¹/₂ of them accepted the books, and each accepted 6 books, which is 3 books per member on average.

Similarly, it doesn't matter how many non-members there were as ³/₄ of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.

Double-Checking
Both the members and non-members accepted, on average, 3 books each.

And 1400 x 3 = 4200.

Workings

Hint
The first letters of the words are: C, F, J, M, M, P, P, T, W, Z (but not in this order).

Answers
Japan    = 1010 + 1 + 10000 + 1 + 1110 Wales    = 10111 + 1 + 1100 + 101 + 10011 Poland   = 10000 + 1111 + 1100 + 1 + 1110 + 100 France   = 110 + 10010 + 1 + 1110 + 11 + 101 Chile    = 11 + 1000 + 1001 + 1100 + 101 Morocco  = 1101 + 1111 + 10010 + 1111 + 11 + 11 + 1111 Zambia   = 11010 + 1 + 1101 + 10 + 1001 + 1 Tonga    = 10100 + 1111 + 1110 + 111 + 1 Panama   = 10000 + 1 + 1110 + 1 + 1101 + 1 Mongolia = 1101 + 1111 + 1110 + 111 + 1111 + 1100 + 1001 + 1

Workings

Hint
Where else might you see arrows and letters together?

Answers
See, new, sense, sew, ewe.

The arrows are pointing in the compass directions N, E, S, and W.

Workings

Hint
Look at the first and third columns first.

Answer
The missing sum is 40.
Circle   = 12
Star     = 3
Square   = 7
Triangle = 9

Reasoning
Looking at Column 1 and Column 3 we have:

[1]   Square + Star + Circle + Square = 29
[2]   Square + Square + Triangle + Star = 26

If we subtract [1] − [2] we get:

[3]   Circle − Triangle = 3

And Row 3 is:

[4]   Circle + Circle + Triangle + Circle = 45

If we add [3] + [4] we get:

Circle + Circle + Circle + Circle = 48

So, Circle = 12.

Using [3] we find that Triangle = 9.

Using Column 2 we find that Star = 3.

Using Row 1 we find that Square = 7.

Double-Checking
The rows add to: 35 + 26 + 45 + 25 = 131.

The columns add to: 29 + 36 + 26 + 40 = 131.

The rows and columns must add to the same number, so this could have been used a shortcut to the missing sum.

In total, there are:
   5 Squares   = 5 x 7  = 35
   5 Circles   = 5 x 12 = 60
   3 Stars     = 3 x 3  =  9
   3 Triangles = 3 x 9  = 27

Which is also a total of 131.

So all of the totals are the same, as expected.