Random Puzzles 

Workings

Hint
The first missing letter is S.

Answer
A stitch in time saves nine.

Workings

Hint
Try starting with the cube root of the number.

Answer
42, 44, and 46.

Reasoning
As we require 3 numbers that are multiplied together, we can start with the cube root of 85,008 ≈ 43.97.

We can now check that 44 divides 85,008 exactly: 85,008 ÷ 44 = 1,932, which means that 44 is likely to be one of the numbers.

And as we know that we need consecutive even numbers, we soon find 42 and 46 as the remaining numbers.

Double-Checking
42 x 44 x 46 = 85,008.

Workings

Hint
How old was the person in second place?

Answer
# Name    Age
1 Drew    30
2 Emery   24
3 Glen    27
4 Alex    32

Reasoning
By (2), because Glen was three years older, the person in 2^nd place was either 24 or 27.

But 2^nd place can't have been 27, because, by (4), Emery was ahead, but didn't win.

So 2^nd place was 24, and Glen was 27.

By (3), Drew could only be 27 or 30, but we now know what Glen was 27, so Drew was 30.

By (1), the person who came last was 32:
1
2         24
3
4         32

By (4), the 27-year-old can't have won,
1 Drew    30
2         24
3 Glen    27
4         32

By (4), Emery beat the 27-year-old:
1 Drew    30
2 Emery   24
3 Glen    27
4         32

Leaving Alex in last place.
1 Drew    30
2 Emery   24
3 Glen    27
4 Alex    32

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.