Random Puzzles 

Workings

Hint
Try this with a real board.

Answer
5 queens are required.

Workings

Hint
If we look at all of the clues, each person appears exactly twice.

Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.

Reasoning
If we look at all of the clues, each person appears exactly twice.

So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.

So, Alex + Billie + Charlie = 43 years.

In each clue we are given two of the people, so we can use this to find the missing person:

   Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 − 22 = 21 years.

   Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 − 28 = 15 years.

   Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 − 36 = 7 years.

Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:

[1]   A + B = 36
[2]   C + B = 22
[3]   C + A = 28

If we use [3] − [2] we have:

[4]   A − B = 6

If we use [1] + [4] we have:

   2A = 42
    A = 21

By [1] B = 15. By [3] C = 7.

Workings

Hint
This is a trick question.

Answer
Once.

After which you will be taking 7 from 42!

Workings

Hint
A fathom is 6 feet.

Answer
Hours in a month.

Reasoning
A fathom is 6 feet, which is 1.8288 metres.

So there are 1000 ÷ 1.8288 ≈ 546.8 fathoms in a kilometre.

The shortest month has 28 x 24 hours = 672.

So even the shortest month has more hours than there are fathoms in a kilometre.