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Workings

Hint
Can Q1 be A?

Answers
Q1. B
Q2. B
Q3. A
Q4. B

Reasoning
Q1 can't have A as its answer (otherwise it would contradict itself).

If Q1's answer was C (meaning Q4's answer was A), then Q3's answer would be C. However, Q2's answer should now be A, but this isn't allowed by Q1 (as Q4 is the first answer with A). This is a contradiction.

Therefore, Q1's answer is B (meaning Q3's answer is A).

For Q2's answer to be C, Q4's answer would have to be A, which would contradict Q4. Therefore, Q2's answer is B making Q4's answer B.

Workings

Hint
You might find Pythagoras' theorem very useful [a² + b² = c²].

Answer
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.

Workings

Hint
In the word LOG, why might the L have be replaced with 50?

Answer
FO10.

Reasoning
If there is a Roman numeral, it is replaced by its modern equivalent.
   I = 1
   V = 5
   X = 10
   L = 50
   C = 100
   D = 500
   M = 1000

Double-Checking
CLICK = 100 50 1 100 K MILK  = 1000 1 50 K LOG   = 50 O G LIFE  = 50 1 F E ALIVE = A 50 1 5 E FOX   = F O 10

Workings

Hint
Don't forget the extra 9's in 90, 91, etc.

Answer
300.

Reasoning
Start with: 9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99 – which is 20 9's.

We then repeat this for 100, 200, 300, up to 900 – which is 200 9's.

But from 900 to 999 we have an extra 100 9's as each starts with a 9.

So the total is 300.