Random Puzzles 

Workings

Hint
Count carefully!

Answer
There are 10 letter Fs.

Sometimes the F in 'of' aren't always counted.

Workings

Hint
V represents a vowel (AEIOU).

Answer
A stitch in time saves nine.

Each vowel (AEIOU) is represented by the letter V and each consonant is represented by C.

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
Adding the speeds won't work.

Answer
205 mph.

Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.

The first ²⁄₅ are covered at 123 mph. Therefore, the time taken was [(²⁄₅) x L] ÷ 123 hours.

The next ²⁄₅ are covered at 164 mph. Therefore, the time taken was [(²⁄₅) x L] ÷ 164 hours.

The last ¹⁄₅ is covered at y mph. Therefore, the time taken was [(¹⁄₅) x L] ÷ y hours.

The entire trip is covered at an average of 150 mph, and we can conclude that:
 2L      2L      L     L
————— + ————— + ——— = ———
5x123   5x164    5y   150

Rearranging and simplifying gives:
 1     1    2     2
——— = —— - ——— - ———
 y    30   123   164

That means that y = 1 ÷ (¹⁄₃₀ − ²⁄₁₂₃ − ²⁄₁₆₄)

Using a calculator gives y = 205.