Answer: Sparkle = 4p
Wibbler = 23p
Nobbler = 13p
If we label the clues.
A Nobbler is over three times the price of a Sparkle. [1]
Six Sparkles are worth more than a Wibbler. [2]
A Nobbler, plus two Sparkles costs less than a Wibbler. [3]
A Sparkle, a Wibbler and a Nobbler together cost 40p. [4]
By [3] a Nobbler, plus two Sparkles costs less than a Wibbler, a Wibbler must be the most expensive sweet.
By [1] 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 [2] a Wibbler could only be up to 5p, by [4] 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 [2] a Wibbler could only be up to 11p, by [4] 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 [2] a Wibbler could only be up to 17p, by [4] 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 [1] a Nobbler must be at least 13p, by [4] 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 [4] a Wibbler would cost 22p. This would not satisfy [3]. And if we increase the price of a Nobbler, [3] is never satisfied.
If a Sparkle was 5p, by [1] a Nobbler must be at least 16p, by [4] making a Wibbler at most 19p. This would not satisfy [3].
If we increase the price of a Sparkle or Nobbler further, [3] is will never be satisfied.
Therefore the only solution we came across must be the correct one.
At the local sweet shop, three particularly nice sweets are on special offer.
What number do you get if...
What does this equation simplify to?
