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Workings

Hint
What dries?

Answer
A towel.

Workings

Hint
The anagrammed word begins with the letter S.

Answers
Spaghetti.
--xic = toxic --ien = alien --nre = genre --ppo = hippo --pil = pupil --loo = igloo --day = today --uip = equip --elf = shelf
Giving the letters TAGHPITES, which is an anagram of SPAGHETTI.

Workings

Hint
How can we write this time and date?

Answer
The time and day became:

12:34 5/6/78 (in UK format)

In US format, this happened on the 6^th of May.

Workings

Hint
There are two different methods, one involves a cube root, and the other doesn't require a calculator.

Answer
9 x 11 x 13.

Reasoning #1
We're after three numbers that multiply together, so a good place to start is the cube root of 1,287, which is roughly 10.88.

Let's try dividing by the closest odd number to 10.88:

   1287 ÷ 11 = 117

We're now after whole divisors of 117. Trying the odd numbers either side of 11 might work.

Trying either 9 or 13 gives the answer:

   9 x 11 x 13 = 1,287

Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.

Reasoning #2
We after three numbers that multiply together, but none of these can end in 5 (otherwise our answer would end in 0 or 5).

So, they can only end in 7, 9, 1 (e.g. 87, 89, 91), or 9, 1, 3 (e.g. 89, 91, 93).

However, if they ended in 7, 9, 1, the answer would end in 3 (because 7 x 9 x 1 = 63).

Therefore, they end in 9, 1, and 3 (because 9 x 1 x 3 = 27).

The first numbers we can try are 9, 11, 13:

   = 9 x 11 x 13
   = 99 x 13
   = 100 x 13 - 13
   = 1300 - 13
   = 1,287

A calculator is not required!