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Hint: Tops of thermometers can't be filled unless the bottoms are.
Answer:
Puzzle 22
The other day I was sitting in my local tavern, The Spyglass, which overlooks the sea, when in sailed my old friend the pirate Captain Conan Drum. "Well, shiver me barnacles!" he roared on seeing me. He too is a bit of a puzzle addict and so, after joining me for a glass of milk and telling me about his latest exploits on the high seas, he couldn't resist showing me his latest conundrum.
He reached into one of his jacket pockets and produced seven gleaming £5 coins, which he then proceeded to arrange on the table in front of me exactly as shown below. "Now, me lad." he said, with a mischievous look in his eyes. "I'll wager you'll not be able to solve this one. Take away two coins from this here arrangement to leave five coins across and three coins going down."
It was clear the wily old sea dog still had one or two tricks up his sleeve, as I couldn't for the life of me see how it could be done. Can you see through his skulduggery and solve it?
Answer:
Take away the two coins on the right end of the row of five coins to leave 'five coins, a cross and three coins going down'.
I fell into his trap and misinterpreted what he was actually asking me to do!
Puzzle 23
The surface area of a spherical balloon measured in square inches is the same as its volume, measured in cubic inches. What is the diameter of the balloon?
[Ref: ZEZW]
Hint: The volume of a sphere is (4/3) * Pi * (r^3).
Answer: 6 inches. The surface area of a sphere, of radius r, is 4 * Pi * (r ^ 2) and the volume is (4/3) * Pi * (r^3). Putting these equal and cancelling gives r = 3, which means the diameter is 6 inches. QED.
Puzzle 24
Three people are buried in the sand all facing forwards with their heads above ground.
Each person has a hat placed on their head selected from a bag containing 3 red hats, and 2 black hats, and they knew the possible hat choices.
They cannot turn around to see those behind them.
The person at the back is asked what hat they are wearing. They reply 'I do not know'. The middle person is asked what hat they are wearing. They also reply 'I do not know'. The person at the front is then asked what hat they are wearing. They reply 'I am wearing a red hat'.
How did they know?
[Ref: ZSAU]
Hint: Think about the person at the back first.
Answer:
Since the person at the back could not determine their own hat, this means that the front two people could not both have been wearing black hats and that, therefore, there must be at least one red hat on the two front people.
Therefore the middle person must not be able to see a black hat otherwise they would know they had a red one on.
Therefore the front person must be wearing a red hat  which finally they deduce. Interestingly, the other two can never determine their own hats.
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