Brain Teasers and Puzzles 

Workings

Hint
Remember that each person told exactly one truth and exactly one lie.

Answer
Drew.

Reasoning
Since each suspect told the truth just once, Emery's statements mean that it was either Drew or Alex.

If it was Alex, then both of Billie's statements would be true, which isn't allowed (and similarly both of Drew's would be false).

Therefore, it was Drew.

This can be double-checked with all of the other statements.

Workings

Hint
From the 1 go straight down.

Answer

Workings

Hint
Which sweet is the least expensive?

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

If we label the clues.

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

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.

Workings

Hint
The first word is BEARD.

Answer
-e-rd + ba = beard -u-et + qi = quiet wa-t- + lz = waltz -um-y + jp = jumpy -e-er + fv = fever a-o-e + wk = awoke mi--d + xe = mixed -hew- + cy = chewy hu-i- + md = humid -abi- + ht = habit co--h + ug = cough ho--e + rs = horse arg-- + on = argon