Random Puzzles 

Workings

Hint
Be careful with the middle of the last word.

Answer
Business.
Committee.
Sincerely.
Archaeologist.

Workings

Hint
There are two different methods, one involves a cube root, and the other doesn't require a calculator.

Answer
9 x 11 x 13.

Reasoning #1
We're after three numbers that multiply together, so a good place to start is the cube root of 1,287, which is roughly 10.88.

Let's try dividing by the closest odd number to 10.88:

   1287 ÷ 11 = 117

We're now after whole divisors of 117. Trying the odd numbers either side of 11 might work.

Trying either 9 or 13 gives the answer:

   9 x 11 x 13 = 1,287

Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.

Reasoning #2
We after three numbers that multiply together, but none of these can end in 5 (otherwise our answer would end in 0 or 5).

So, they can only end in 7, 9, 1 (e.g. 87, 89, 91), or 9, 1, 3 (e.g. 89, 91, 93).

However, if they ended in 7, 9, 1, the answer would end in 3 (because 7 x 9 x 1 = 63).

Therefore, they end in 9, 1, and 3 (because 9 x 1 x 3 = 27).

The first numbers we can try are 9, 11, 13:

   = 9 x 11 x 13
   = 99 x 13
   = 100 x 13 − 13
   = 1300 − 13
   = 1,287

A calculator is not required!

Workings

Hint
Start on any square, and see how far you can get.

Answer
Start from the 2U in the bottom right-hand corner.

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 and 7 x 2 = 14.

6 x 8 = 48 and 4 x 8 = 32.

8 x 8 = 64 and 6 x 4 = 24.