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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
How many 1 x 1 squares are there?

Answer
91 squares.

Reasoning
Squares of size:
   1 x 1 = 36
   2 x 2 = 25
   3 x 3 = 16
   4 x 4 = 9
   5 x 5 = 4
   6 x 6 = 1

Total = 36 + 25 + 16 + 9 + 4 + 1 = 91.

Workings

Answer
Kevin, Neil and Larry.

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.