Random Puzzles 

Workings

Hint
Remember that there are 12 inches in a foot.

Answer
I asked for 9 foot 2 inches (110 inches) and my friend brought me 2 foot 9 inches (33 inches).

Reasoning
I asked my friend to buy me A feet and B inches, which is a total of 12A + B inches.

He accidentally bought me B feet and A inches, which is 12B + A inches.

We know that 12B + A is actually only 30% of what I wanted, so:

     12B + A = 0.3 x (12A + B)

Multiply throughout by 10:

  120B + 10A = 3 x (12A + B)

  120B + 10A = 36A + 3B

        117B = 26A

           B = 26A ÷ 117

Don't forget that A and B can only be integers, and between 0 and 11.

Since 26 x A has to be at least 117, the lowest possible value for A is 5. We can check the remaining possibilities.
 5 x 26 = 130
 6 x 26 = 156
 7 x 26 = 182
 8 x 26 = 208
 9 x 26 = 234 (*)
10 x 26 = 260
11 x 26 = 286

The only number wholly divisible by 117 is 234, which means that A = 9, and B = 2.

So, I originally asked for 9 feet 2 inches.

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
Where on Earth can you end up back where you start?

Answer
White.

They were at the north pole and saw a polar bear.

Workings

Hint
A little algebra might help.

Answer
Width=40, height=20, depth=18.

Reasoning
If we call the height H, the width W and the depth D we have:
   H x W = 800

       H = 800 ÷ W (1)

   W x D = 720

       W = 720 ÷ D (2)

   H x D = 360

       H = 360 ÷ D (3)

Using (1) and (3) we have:
   800   360
   ——— = ———
    W     D

   800 x D = 360 x W

Using (2):
   800 x D = 360 x 720
                   ———
                    D

   800 x D² = 259,200

         D² = 324

          D = 18

Using (2), W = 40.

Using (1), H = 20.