Over the last few hundred years there have been thousands of reported incidents of horses jumping over towers and landing on clergy and small men, forcing their removal.

These incidents are well documented and there is great evidence that they all happened.

How can this be explained?

[Ref: ZKFP]

Hint: This happens in a game - which one though?

Answer:
In a game of chess! This occurs when a knight, which looks like a horse, takes a bishop or a pawn.

Puzzle 418

How many grains of sand do you need until you have a heap of sand?

[Ref: ZMQO]

Hint: Is a million grains of sand a heap?

Answer: We can safely say two things:

1. A million grains of sand is a heap.
2. If we remove one grain of sand from a heap, we still have a heap.

We can now keep repeating #2 until we only have a single grain of sand remaining. Is this a heap? Clearly not. But what went wrong with our thinking?

This is called the Sorites paradox (soros being Greek for "heap"), and is a classic paradox that has no real answer. Both #1 and #2 are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. When does the heap become a non-heap? If we remove one more grain we're left with nothing, is this still a heap?

Puzzle 419

A farmer was asked how many chickens he had sold at market that day. His reply was:

I've had four customers today, and each bought half of my remaining chickens, plus a half chicken.

The farmer sold all of his chickens at market that day. How many chickens did the farmer sell?

Hint: How many chickens did the last customer buy?

Answer: 15 chickens.

The first customer bought 15 ÷ 2 + ½ = 8 (leaving 7)
The second customer bought 7 ÷ 2 + ½ = 4 (leaving 3)
The first customer bought 3 ÷ 2 + ½ = 2 (leaving 1)
The first customer bought 1 ÷ 2 + ½ = 1

The answer can be worked out in the following way:

The fourth customer can only have bought one chicken, otherwise there would be some chickens left. The third customer bought all but 1, so total - (total ÷ 2 + ½) = 1. This can be solved algebraically or it's easy to see that the total must have been 3. This method keeps working until we reach the first customer.

Puzzle 420

Using the BrainTracker grid below, how many words can you find? Each word must contain the central S and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?