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

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.

Can you determine the price of each type of sweet?

Puzzle Copyright © Kevin Stone

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Hint

Which sweet is the least expensive?

Answer

Sparkle = 4p

Wibbler = 23p

Nobbler = 13p

Reasoning

By (3) a Nobbler, plus two Sparkles costs less than a Wibbler, therefore a Wibbler must be the most expensive sweet.

By (1) a Nobbler is over three times the price of a Sparkle, therefore a Sparkle must be 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.

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