Random Puzzles 

Workings

Hint
There are 13 loaves in a baker's dozen.

Answer
Loaves in a dozen baker's dozen.

Reasoning
A baker's dozen is 13, so a dozen baker's dozen is:

   12 x 13 = 156 loaves

There are 15 red balls in snooker, and each of these can be followed by the black ball, and then the colours in order gives:

   15 x (1 + 7) + 2 + 3 + 4 + 5 + 6 + 7 = 147 points

This can rise to 155 if the break follows a foul.

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.

Workings

Hint
How many rations were there at the start?

Answer
30 days.

Reasoning
Originally there was enough food for 220 people for 21 days, which totals 4620 rations.

After 6 days 1320 rations were eaten.

Therefore, there were now 3300 rations for 275 people, which would last for another 24 days at one-half ration per person.

Which is 30 days in total from the original sinking.

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.