Random Puzzles 

Workings

Hint
What must the middle temperature be? Remember that the temperature are in degrees Celsius.

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

Each day 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 matches 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.

Workings

Hint
Try working backwards.

Answer
£98.82.

Reasoning
At the end I was left with £32.94, which was half of my remaining money, so before buying the trousers I must have had £65.88.

Again, this was half of my money, so before buying the jacket I must have had £131.76 at the start.

As I now had £32.94 remaining, I must have spent £98.82.

Double-Checking
I started with £131.76, and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82.

Workings

Hints
The first letters of the words are: E, S, P, C, I, A, P, A.

Answers
-----yee = employee -----egy = strategy -----igm = paradigm -----lse = convulse -----com = intercom -----bet = alphabet -----lel = parallel -----dee = attendee

Workings

Hint
One of the words is waterfall (wat + erf + all).

Answers
som + eth + ing = something
hai + rbr + ush = hairbrush
gra + ssl + and = grassland
pin + eap + ple = pineapple
pol + ice + man = policeman
mea + nwh + ile = meanwhile
wat + erf + all = waterfall
sca + rec + row = scarecrow
yes + ter + day = yesterday
obs + tin + ate = obstinate