Random Puzzles 

Workings

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?



Not 3, because the difference between 1 and 3, and the difference between 3 and 5, are both D2.
Not 4, because the difference between 4 and 5 is D1, which we would already have.
Not 6, 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:

Workings

Hint
Look at the second letter in each word.

Answer
Guava.

The second letter of the words are the vowels (AEIOU) in order.

Workings

Hint
We'll assume that we can actually fold it this many times.

Answer
Very thick indeed! The paper doubles in thickness with each fold. If we could fold it 50 times, it would be around 70 million miles thick!

1 fold would be 0.1 + 0.1 = 0.1 x 2 ^ 1 = 0.2 mm
2 folds would be 0.1 + 0.1 + 0.1 + 0.1 = 0.1 x 2 ^ 2 = 0.4 mm
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10 folds would be 0.1 x 2 ^ 10 = 102.4 mm
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50 folds would be 0.1 x 2 ^ 50 = 112,589,990,684,262.4 mm = 112,589,990.7 km (around 70 million miles).

Workings

Hint
Look at the first and third columns first.

Answer
The missing sum is 40.
Circle   = 12
Star     = 3
Square   = 7
Triangle = 9

Reasoning
Looking at Column 1 and Column 3 we have:

[1]   Square + Star + Circle + Square = 29
[2]   Square + Square + Triangle + Star = 26

If we subtract [1] − [2] we get:

[3]   Circle − Triangle = 3

And Row 3 is:

[4]   Circle + Circle + Triangle + Circle = 45

If we add [3] + [4] we get:

Circle + Circle + Circle + Circle = 48

So, Circle = 12.

Using [3] we find that Triangle = 9.

Using Column 2 we find that Star = 3.

Using Row 1 we find that Square = 7.

Double-Checking
The rows add to: 35 + 26 + 45 + 25 = 131.

The columns add to: 29 + 36 + 26 + 40 = 131.

The rows and columns must add to the same number, so this could have been used a shortcut to the missing sum.

In total, there are:
   5 Squares   = 5 x 7  = 35
   5 Circles   = 5 x 12 = 60
   3 Stars     = 3 x 3  =  9
   3 Triangles = 3 x 9  = 27

Which is also a total of 131.

So all of the totals are the same, as expected.