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
Sometimes the easiest explanations are the best.

Answer
The other end of the rope is not tied to anything!

Workings

Hint
Try working backwards.

Answer
148.

Reasoning
A number that is divisible by 3 has digits that add up to a number that is also divisible by 3 (for example, 123 is divisible by 3).

So we can look for the first number where 4 + 4 + 4 + 4 + 4 + ... is divisible by 3, which is 4 + 4 + 4, and 444 ÷ 3 = 148.

Alternative Reasoning
Let's try the possible answers in order:

  4 ÷ 3 = 1.3333
 44 ÷ 3 = 14.6666
444 ÷ 3 = 148

Double-Checking
148 x 3 = 444.

Workings

Hint
The word starts with B.

Answer
Border becomes boarder.