Random Puzzles 

Workings

Hints
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

Workings

Hint
The list is related to numbers.

Answer
Llama.

The length of each word is the same length as the numbers one, two, three, four, five, six, etc.

The next number is SEVEN, which has 5 letters, and llama is the only word with 5 letters.

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 must the middle midday temperature be? Remember that the temperatures are in degrees Celsius.

Answer
The midday temperatures were -6, -2, 2, 6, 10 °C.

Each day the midday temperature increased by a steady 4 degrees.

Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).

Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).

If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.

If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does match all of the requirements.

If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.

Any larger increase makes the product even larger, so we can stop checking.

So the only possible answer is -6, -2, 2, 6, 10.