Random Puzzles 

Workings

Hint
How many rooms can Alex clear in 36 hours?

Answer
12 hours.

Reasoning
In 36 hours, Alex could empty 2 lots of bookshelves, Billie could also empty 2 lots of bookshelves, and Drew could refill 1 lot of bookshelves.

So, 2 + 2 − 1 = 3 lots of bookshelves in 36 hours. Which is 12 hours for one lot of bookshelves.

Alternative Reasoning
Alex and Billie can each empty ¹/₁₈ of the bookshelves in 1 hour, but Drew will refill ¹/₃₆ of the bookshelves in one hour.

So in one hour we have ¹/₁₈ + ¹/₁₈ − ¹/₃₆ = ¹/₁₂.

So it would take 12 hours to empty the bookshelves.

Workings

Hints
The first letters of the words are: M, C, C, S, V, G, A, T, S, T, S, F, S, D, O.

Answers
---rix = matrix ---osy = choosy ---few = curfew ---oze = snooze ---uum = vacuum ---wth = growth ---nda = agenda ---nis = tennis ---tem = system ---pod = tripod ---reo = stereo ---hom = fathom ---gan = slogan ---amt = dreamt ---gen = oxygen

Workings

Hint
The first answer is Aaron.

Answer
rn   = Aaron or Ernie or Ron
jms  = James
kvn  = Kevin
smn  = Simon
kth  = Keith
jrmh = Jeremiah

Workings

Hint
What could we do with the digits?

Answer
If the sum of the digits is divisible by nine, so is the number.

Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.

For example, is 486451464 divisible by 9?

Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.

Is 42 divisible by 9? Not sure, you can then do:

4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.