Answers to last issue's Brain Teasers
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After a local Post Office burglary, five suspects were being interviewed.

Below is a summary of their statements.

Police know that each of them told the truth in one of the statements and
lied in the other.

From this information can you tell who committed the crime?

    Brian said:
       It wasn't Charles
       It was Alan

    Derek said:
       It was Charles
       It wasn't Alan

    Charles said:
       It was Brian
       It wasn't Eric

    Alan said:
       It was Eric
       It wasn't Brian

    Eric said:
       It was Derek
       It was Alan 

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[Ref: ZQRF] © Kevin Stone 
Hint: Remember that each person told exactly one truth and exactly one lie.
Answer: Derek was the culprit.

Looking at Brian's statement if it was Charles, then Brian was lying in his first statement, which makes the second statement true. Which would mean that it was both Charles and Alan. So it can't be Charles.
Which means Derek was lying in his first statement, which makes the second statement true. Therefore it can't be Alan.
So Eric's second statement must be false, meaning his first statement was true, therefore it was Derek.

2.
If you are in a dark room with a candle, a wood stove and a gas lamp.

You only have one match, so what do you light first?

Ans: The match

3. Complete the fifth circle with the correct dots. 

Ans: Answer:
At each stage, a new dot starts at the top, and then goes either clockwise,
or counter-clockwise.

4. A rope swing hangs vertically down so that the end is 12 inches from the
ground, and 48 inches from the tree.

If the swing is pulled across so that it touches the tree, it is 20 inches
from the ground.

How long is the rope? 

Ans: 148 inches
We can use Pythagoras' theorem if we draw an imaginary line across to
create a right-angled triangle.

The hypotenuse is equal to the rope's length R. The bottom of the triangle
is 48 inches. The vertical side is R - 8 (the difference between 20 inches
and 12 inches).

Pythagoras' theorem tells us that:

   a2 + b2 = c2

Where c is the hypotenuse.

This gives us:

          482 + (R - 8)2 = R2

   2304 + (R - 8)(R - 8) = R2

    2304 + R2 - 16R + 64 = R2

         2304 - 16R + 64 = 0

                     16R = 2368

                       R = 148

As required. QED.