Random Puzzles 

Workings

Hint
The eleven-letter word begins with the letter I.

Answer
Investigate.
bake = bike swap = snap opal = oval dyed = deed idle = isle snow = stow lump = limp aces = ages melt = malt spun = stun rant = rent

Workings

Hint
The answer involves multiplication (for example, 9 x 8 = 72).

Answer
468.

Reasoning
If we split each line in the following way:

98 68 88
72 48 64
14 32 24

Each new line is generated by multiplying the digits two at a time and writing the result below.

For example, 9 x 8 = 72, so 72 appears directly below 98.

And 7 x 2 = 14, so 14 appears directly below 72.

Double-Checking
9 x 8 = 72, 7 x 2 = 14, 1 x 4 = 4.

6 x 8 = 48, 4 x 8 = 32, 3 x 2 = 6.

8 x 8 = 64, 6 x 4 = 24, 2 x 4 = 8.

Workings

Hint
How many 2 x 2 squares are there?

Answer
There are 93 squares without a rook.

Reasoning
There are 60 squares of size 1 x 1.
There are 33 squares of size 2 x 2.

Giving a total of 60 + 33 = 93 squares.

Workings

Hint
Is there a missing letter?

Answer
Attempts.

This word contains the only letter E in the entire paragraph, notice how every other letter appears at least once.

Although the letters C, E, J, Q, V, X each all appear once, the longer the piece of text the more difficult it is to avoid the letter E.