## 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...

- Red Chad in revolt
- It’s made backwards =
*Edam*
- Greek as fate turns out
- The one after boulder three =
*Roquefort*
- French author follows mythical beast

### 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.