Mathematical Puzzles 

Workings

Hint
There is a little trick to this puzzle.

Answer
2 + 13 + 2 = 17.

The puzzle didn't ask for three digits to be circled!

Workings

Hint
Try working backwards.

Answer
335 strawberries.

Reasoning
Working backwards...

I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.

I ate 6 myself, so I had 108 before I ate those.

I had 108 strawberries, so I had 162 before giving Billie one third.

I ate 3 myself, so I had 165 before I ate those.

I had 165 strawberries, so I had 330 before giving Alex one half.

Ate 5 myself, so I had 335 before I ate those.

Therefore, I started with 335 strawberries.

Double-Checking
I started with 335.

I ate 5, leaving 330.

I gave Alex half (165), leaving 165.

I ate 3, leaving 162.

I gave Billie one third (54), leaving 108.

I ate 6, leaving 102.

I gave Charlie two thirds (68), leaving 34.

Workings

Hint
How large would the smaller cube be?

Answer
1,352 small cubes.

Reasoning
The original large cube with 16 small cubes along each edge would require 16 x 16 x 16 = 4,096 small cubes.

Removing the outside layer would leave a large cube now with 14 small cubes along each edge (which requires 14 x 14 x 14 = 2,744 small cubes).

It isn't 15 small cubes because you're removing both ends of an edge.

Therefore, you have removed 4,096 – 2,744 = 1,352 small cubes.

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).