Random Puzzles 

Workings

Hint
What does each one do?

Answer
Door.

The others are used to cover windows.

Workings

Hint
It might be easier to work backwards.

Answer
£50.

Reasoning
Working backwards:

On Thursday, I had £12.50.

On Wednesday, I had £12.50 x (1 ÷ one half) = £25.

On Tuesday, I had £25 x (1 ÷ two thirds) = £37.50.

On Monday, I had £37.50 x (1 ÷ three quarters) = £50.

Workings

Hint
What do the fractions add up to?

Answer
There are 980 coins in the collection.

Reasoning
Using fractions:

   ¹/₂ + ¹/₄ + ¹/₅ = ¹⁹/₂₀

The remaining ¹/₂₀ is 49 coins.

Therefore, the ²⁰/₂₀ must equal 20 lots of 49 = 980.

Alternative Reasoning
Using percentages:

   50% + 25% + 20% = 95%

The remaining 5% is 49 coins.

If 5% is 49 coins, 10% is 98 coins, 100% is 980 coins.

Double-Checking
¹/₂ of 980 is 490
¹/₄ of 980 is 245
¹/₅ of 980 is 196
and the remaining 49 coins.

And 490 + 245 + 196 + 49 = 980.

Workings

Hint
Convert the letters to positions in the alphabet.

Answer
M.

Reasoning
These are letters that occupy prime number positions in the alphabet:
b =  2
c =  3
e =  5
g =  7
k = 11
m = 13 *
q = 17
s = 19
w = 23