Brain Teasers and Puzzles 

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
The first word is base.

Answer
Strawberry.
bake = base cure = cute maze = mare pest = peat neat = newt rope = robe port = poet food = ford poke = pore soda = soya

Workings

Hint
One of the words is SAUSAGE.

Answers
Sixteen, shampoo, seaweed, sausage, spanner, speaker, syringe, snorkel.

Workings

Hint
Think of the pages from 1-9, and then 10-99.

Answers
There are 147 pages. The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.

For pages 10-99, there are 90 pages, which is 180 digits.

This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.

Taking us to 9 + 90 + 48 = 147 pages in total.

Answer #2
From page 1 to 147 we have 15 pages that end in 3:

   3, 13, 23, ..., 143

We also have the ten pages that start with 30:

   30, 31, 32, ..., 39

Plus the ten pages that start with 130:

   130, 131, 132, ..., 139

For a total of 15 + 10 + 10 = 35 number 3's.