 # Puzzle ZQVP ??

## Puzzle Details

At the local sweet shop, three particularly nice sweets are on special offer.

A Sparkle, a Wibbler and a Nobbler together cost 40p.
A Nobbler is over three times the price of a Sparkle.

Six Sparkles are worth more than a Wibbler.

A Nobbler, plus two Sparkles costs less than a Wibbler.

Can you determine the price of each type of sweet?

Sparkle =  4p
Wibbler = 23p
Nobbler = 13p

If we label the clues.

   A Nobbler is over three times the price of a Sparkle.
   Six Sparkles are worth more than a Wibbler.
   A Nobbler, plus two Sparkles costs less than a Wibbler.
   A Sparkle, a Wibbler and a Nobbler together cost 40p.

By  a Nobbler, plus two Sparkles costs less than a Wibbler, a Wibbler must be the most expensive sweet.

By  a Nobbler is over three times the price of a Sparkle, a Sparkle is cheaper than a Nobbler and hence the cheapest sweet.

So the order of sweets, from the least to most expensive, is Sparkle, Nobbler, Wibbler.

If a Sparkle was 1p, by  a Wibbler could only be up to 5p, by  a Nobbler would cost at least 34p, which is more than a Wibbler and isn't allowed as the Wibbler is the most expensive sweet.

If a Sparkle was 2p, by  a Wibbler could only be up to 11p, by  a Nobbler would cost at least 27p, which is more than a Wibbler and isn't allowed as the Wibbler is the most expensive sweet.

If a Sparkle was 3p, by  a Wibbler could only be up to 17p, by  a Nobbler would cost at least 20p, which is more than a Wibbler and isn't allowed as the Wibbler is the most expensive sweet.

So a Sparkle must be at least 4p.

If a Sparkle was 4p, by  a Nobbler must be at least 13p, by  a Wibbler would cost 23p - this combination matches all of the clues and is a possible solution.

If a Sparkle was 4p and a Nobbler 14p, by  a Wibbler would cost 22p. This would not satisfy . And if we increase the price of a Nobbler,  is never satisfied.

If a Sparkle was 5p, by  a Nobbler must be at least 16p, by  making a Wibbler at most 19p. This would not satisfy .

If we increase the price of a Sparkle or Nobbler further,  is will never be satisfied.

Therefore the only solution we came across must be the correct one.