Random Puzzles 

Workings

Hint
Tops of thermometers can't be filled unless the bottoms are.

Answer
 

Workings

Hint
There are fewer than 1,000 apples.

Answer
946 apples.

Reasoning
We know that (answer – 1) is divisible by 3, 5, 7, and 9.

If it's divisible by 9 then it's automatically divisible by 3.

So the number must be a multiple of 5, 7, and 9.

   [5 x 7 x 9 = 315]

Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+1).

Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73 – this doesn't work.

Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36 – this doesn't work.

Let's try 3 x 315 + 1: 946 ÷ 11 = 86 – this works and is the answer.

Workings

Hint
What are the possible differences?

Answer
 


Reasoning
The first observation is that all of the possible gaps must exist: 1, 2, 3, 4, 5, 6, 7, and let's call these Gap1, ..., Gap7.

Looking at Gap7, this can only happen when:
   [Gap7a: 1 is next to 8]

Looking at Gap6, this can happen when:
   [Gap6a: 1 is next to 7]
      this is not allowed because 1 and 7 are given squares that are not next to each other.
   [Gap6b: 2 is next to 8]

Looking at Gap5, this can happen when:
   [Gap5a: 1 is next to 6]
   [Gap5b: 2 is next to 7]
      this is not allowed because [Gap6b: 2 is next to 8], which would mean that we can't also have [Gap7a: 1 is next to 8].
   [Gap5c: 3 is next to 8]
      this is not allowed because we couldn't then also have: [Gap7a: 1 is next to 8] and [Gap6b: 2 is next to 8].

We can't have the 8 above the 1, as there is then no place for [Gap6b: 2 is next to 8].

So, we have two possible places for the 8, to the left of the 1, or to the right of the 1.

8 to the left of 1



What can we place to the right of 1?

3 – no, because the gap between the 1 and 3, and the gap between 3 and 5, are both 2.
4 – no, because the gap between 4 and 5 is 1, which we already have.
6 – no, because the gap between 5 and 6 is 1, which we already have.

So the 8 can't go to the left of 1.

8 to the right of 1

We know [Gap5a: 1 is next to 6].

Let's try 6 to the left of 1. No matter where we place the 3 and 4 we end up with duplicate gaps. So this doesn't work.



So, the 6 must go above 1, but the 4 can't go to the left of 1 because of duplicate gaps. Therefore, this doesn't work either.



Which means that the final answer is:

Workings

Hint
A baker's dozen is 13.

Answer
Hours in a week.

Reasoning
A dozen is usually 12, but a baker's dozen is usually 13.

So a dozen (12) baker's dozen (13) = 12 x 13 = 156.

There are 24 hours in a day, and 7 days in a week.

So there are 24 x 7 hours in a week = 168.