Hint
Start by imaging a sign saying 'BrainBashers Puzzles And Illusions'.
Answer
I commissioned an artist to paint a sign for BrainBashers that said 'BrainBashers Puzzles And Illusions', however, they made a terrible mistake.
The gaps between 'Puzzles' and 'And', and 'And' and 'Illusions' weren't the same, so the sign seemed oddly out of balance.
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Puzzle 118
In this puzzle, all of the numbers from 1 to 8 are used.
The differences (larger – smaller) between any two connected numbers are all different.
Can you complete the grid?
Note: this puzzle is not interactive, and cannot be clicked.
Hint
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist. Start by looking where can the 8 go.
Answer
Reasoning
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist: 1, 2, 3, 4, 5, 6, 7, and let's call these D1, …, D7.
D7 can only happen when: 1 is next to 8 = D7
D6 can happen when:
1 is next to 7, but these are given numbers that are not next to each other. 2 is next to 8 = D6
Where can 8 go? If we put 8 above 1, we cannot also satisfy D6 (2 is next to 8).
Therefore, we have two possibilities:
(a) 8 to the left of 1
(b) 8 to the right of 1 (a) 8 to the left of 1
By D6, 2 would be below 8, and this would give us D1, D6, D7. What can we place to the right of 1?
3 – no, because the difference between 1 and 3, and the difference between 3 and 5, are both D2.
4 – no, because the difference between 4 and 5 is D1, which we would already have.
6 – no, because the difference between 5 and 6 is D1, which we would already have.
There are no possible numbers we can place to the right of 1, so 8 can't go to the left of 1. (b) 8 to the right of 1
By D6, 2 would be above 8, and this would give us D3, D6, D7.
4 can't go next to 1, otherwise we'd create another D3. Therefore, 4 goes in the bottom left corner.
We are now left with 3 and 6.
If 6 went above 4, and 3 above 1, these would both be D2.
Therefore, 3 goes above 4, 6 goes above 1.
The final answer is:
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Puzzle 119
Can you find at least 10 different colours hidden in the following paragraph? Can you find all 15?
Many injured animals are invited to live at the 'Toronto Range'. Stop in Kangaroo Corner and marvel at the lovely creatures within. Dig over the potato patch to find small furry caterpillars, but don't yell! Owls can be found swooping for edible nibbles, earwigs, or perhaps bluebottles in the undergrowth. The brown bear, Rob, lacks grace and can look like a sublime ogre, enter at your own risk! Peacocks can be found showing their colourful plumage, which looks fantastic when viewed with our ultraviolet torch.
Many inju[red] animals are invited t[o live] at the 'Toront[o Range]'. Sto[p in K]angaroo [Corn]er and marvel at the lovely creatures with[in. Dig o]ver the potato patch to find small furry caterpillars, but don't [yell! Ow]ls can be found swooping fo[r ed]ible nibbles, earwigs or perhaps [blue]bottles in the undergrowth. The [brown] bear, Ro[b, lack]s grace and can look like a sublime o[gre, en]ter at your own risk! [Pea]cocks can be found showing their colourful [plum]age, which looks fantastic when viewed with our ultra[violet] torch.
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Puzzle 120
Last week I decided to cycle to my Grandparents's house.
On the 1st day, I cycled half of the distance.
On the 2nd day, I cycled one half of the remaining distance.
On the 3rd day, I cycled three quarters of the remaining distance.
On the 4th day, I cycled 10 miles.
On the 5th day, I cycled two thirds of the remaining distance.
