Random Puzzles 

Workings

Hint
The first 6 words begin with the letters D, A, Q, S, W, S.

Answers
---amt = dreamt ---nue = avenue ---rtz = quartz ---oze = snooze ---mth = warmth ---iek = shriek ---gry = hungry ---thm = rhythm ---koo = cuckoo ---spy = crispy ---sip = gossip ---lem = emblem ---uid = liquid ---tyr = martyr ---meg = nutmeg

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
It depends on the length of the word.

Answer
2 buttons.

The number of buttons is 10, minus the length of the word.

Workings

Hint
Look down?

Answer
O.

Every other letter from the top row of a standard keyboard.