Medium Puzzles 

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.

Workings

Hint
Which digit is removed each time?

Answer
97.

Reasoning
The lowest digit is removed each time.

Workings

Hint
The first letters of the words are: T, T, H, D, W, L, H, W, C, N.

Answers
tel + esc + ope = telescope
tim + eta + ble = timetable
hai + rbr + ush = hairbrush
dif + fer + ent = different
wat + erf + all = waterfall
lig + htn + ing = lightning
hea + dli + ght = headlight
whi + rlw + ind = whirlwind
car + til + age = cartilage
new + sag + ent = newsagent