Brain Teasers and 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

Hint
The top number is 186.

Answer
186 x 39 = 7254.

Workings

Hint
Adding 900,000 to the numbner is the same as placing a 9 at the beginning.

Answer
23,076.

Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).

Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).

Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:

 k + 900,000 = 4 x (10k + 9)

 k + 900,000 = 40k + 36

900,000 − 36 = 40k − k

     899,964 = 39k

899,964 ÷ 39 = k

Therefore, k = 23,076.

Double-Checking
923,076 = 4 x 230,769.

Workings

Hint
One answer changes Warm to Worm.

Answer
WARM, WORM, WORK, CORK, COOK, COOL

or

WARM, WORM, WORD, WOOD, WOOL, COOL.