Puzzle Hints and Solutions ...

Diophantus

You could use algebra but a quicker way is to notice that the answer has to be divisible by both 7 and 12 - so the answer might be 84, which can be checked against the facts given.

Looking Backwards

Here are some of the phrases decoded.

GNIKOOL looking backwards
SYMPHON unfinished symphony
DEEF feedback
THINBOXKING thinking outside the box
THATS. thats beside the point

Body Parts

Hint - there are five in the head region, two more in the upper body and the other three are below the waist.

The Frog

The frog makes a net gain of 2m per day so you may think that the answer is 15 days - but check what happens on days 13 and 14.

Hotel Bill

This is just awful accounting. Ask yourself - what did the hotel actually charge for the room; what did the guests pay; and what happened to the difference?

Manhole Cover

Hint - health and safety.

Oh my Brother

The beggar is a woman.

Letter Sequence

O T T F F S S E N

Hint - try initial letters

Five Cheeses

If you like crosswords, this may be for you. What are the following cheeses...


Diamond Ring

Hint - the hasp can take more than one padlock at a time.

Ramanuyan's Number

The number 1729 is the sum of 1 cubed and 12 cubed as well as the sum of 9 cubed and 10 cubed.