Random Puzzles 

Workings

Hint
The area of a circle is π x Radius².

Answers
Circle: 35.

Square: 31.

Triangle: 47.
Doughnut
The area of a circle is π x Radius².

The larger circle has diameter = 40, therefore, the radius is 20, and the area is π x 20² = 400π.

The smaller circle has diameter = 20, therefore, the radius is 10, and the area is π x 10² = 100π.

Therefore, the shaded area is 400π − 100π = 300π ≈ 942.
Circle
The area of a circle is π x Radius².

The circle with diameter 31 has a radius of 15.5 and an area of π x 15.5² ≈ 755.

The circle with diameter 35 has a radius of 17.5 and an area of π x 17.5² ≈ 962 (closest match).

The circle with diameter 39 has a radius of 19.5 and an area of π x 19.5² ≈ 1195.
Square
The area of a square is Side x Side.

The square with side 31 has an area of 31 x 31 = 961 (closest match).

The square with side 35 has an area of 35 x 35 = 1225.

The square with side 39 has an area of 39 x 39 = 1521.
Triangle
The area of a triangle is ¹/₂ x Base x Height. Using Pythagoras' theorem, it can be shown that the area of an equilateral triangle is √3 x Base² ÷ 4.

The triangle with side 39 has an area of √3 x 39 x 39 ÷ 4 ≈ 659.

The triangle with side 43 has an area of √3 x 43 x 43 ÷ 4 ≈ 801.

The triangle with side 47 has an area of √3 x 47 x 47 ÷ 4 ≈ 957 (closest match).

Workings

Hint
Going down and across the floor isn't the only route.

Answer
40 feet.

Explanation Diagram
If you imagine the room to be a cardboard box, you can 'unfold' the room in various ways, and each route gives a different answer.



We can use Pythagoras' theorem (a² + b² = c²) to calculate the distances:
   distance² = horizontal² + vertical²
   distance = √(horizontal² + vertical²)

Route #1
   distance = 1 + 30 + 11 = 42 feet.

Route #2
   horizontal = 6 + 30 + 6 = 42 feet.
   vertical = 10 feet.
   distance = √(42² + 10²) ≈ 43.174 feet.

Route #3
   horizontal = 1 + 30 + 6 = 37 feet.
   vertical = 6 + 11 = 17 feet.
   distance = √(37² + 17²) ≈ 43.178 feet.

Route #4
   horizontal = 1 + 30 + 1 = 32 feet.
   vertical = 6 + 12 + 6 = 24 feet.
   distance = √(32² + 24²) = 40 feet.

Workings

Hint
How many boxes of toys can 1 toy maker make in 5 hours?

Answer
Five toy makers.

Reasoning
How many boxes of toys can 1 toy maker make in 5 hours?
2 toy makers can make 6 boxes of toys in 3 hours
1 toy maker  can make 3 boxes of toys in 3 hours
1 toy maker  can make 1 box   of toys in 1 hour
1 toy maker  can make 5 boxes of toys in 5 hours

So 4 toy makers could only make 20 boxes of toy in 5 hours, and we require the extra toy maker to make the remaining 2 boxes of toys.

Workings

Hint
Start on any square, and see how far you can get.

Answer
Start from the 2U in the bottom right-hand corner.