Puzzle One

If Eli is 173 and Lois is 5107, what is Leslie?

Solution:
From the information given above and the diagram shown below. First, write the names in digital block form and second, rotate each name 180° to read their value or just turn this page up-side-down to read their values directly, including Leslie’s.

Answer: 317537

Puzzle Two

Three identical isosceles triangles fit exactly (without overlap) into a square. Two triangles have one side in common with the square, see below. What is the size of the shaded angle?

Solution:
As the three isosceles triangles are identical, the three angles (which meet in the bottom left-hand corner of the square) are all equal. So each one is 90° ÷ 3 = 30°. In each triangle, the other two angles are equal. Hence each angle equals (180 − 30)° / 2 = 75°.
Therefore, the angle shaded is (90 − 75)° or 15°.

Puzzle Three

The diagram below shows a sequence of shapes made up of black and white floor tiles, where each shape after the first has two more rows plus two more columns than the previous. How many black tiles would be required to create the 15th shape in the sequence?

Solution:
For the 15th shaped diagram, there will be 15 rows of 15 black titles per row plus 14 rows of 14 black tiles per row. Therefore, (15 x 15) + (14 x 14) = 225 + 196 = 421.