## Five Points in a Square

There are 5 points in a square 1×1. Show that 2 of the points are within distance 0.75.

Split the unit square into 4 small squares with side lengths 0.5. At least one of these squares will contain 2 of the points. Since the diagonals of the small squares have lengths less than 0.75, these 2 points must be within such distance.

## Fish in a Pond

There are 5 fish in a pond. What is the probability that you can split the pond into 2 halves using a diameter, so that all fish end up in one half?

Let us generalize the problem to N fish in a pond. We can assume that all fish are on the boundary of the pond, which is a circle, and we need to find the probability that all of them are contained within a semi-circle.

For every fish Fᵢ, consider the semi-circle Cᵢ whose left end-point is at Fᵢ. The probability that all fish belong to Cᵢ is equal to 1/2ᴺ⁻¹. Since it is impossible to have 2 fish Fᵢ and Fⱼ, such that the semi-sircles Cᵢ and Cⱼ contain all fish, we see that the probability that all fish belong to Cᵢ for some i is equal to N/2ᴺ⁻¹.

When N = 5, we get that the answer is 5/16.

## Thoka’s Rebus 4

Can you figure out which word is depicted by this rebus?

The first image on the first row depicts a TEAR. The second image depicts a RAT with a middle letter switched from A to I. From TEARRIT the A is removed, then PILLORY is added, and PILL is removed. The final answer is TERRITORY.

## Pronunciation Puzzles

The following 2 puzzles rely on misleading phrasing of the questions. Read them aloud to your friends and let them ponder upon them.

1. What has 4 letters, sometimes 9, and never 5
2. There are 30 cows and 28 chickens. How many didn’t?
3. Pronounce the following words: T-W-A, T-W-E, T-W-I, T-W-O
4. As I was walking across the London Bridge, I met a man.
He tipped his hat, and drew his cane.
In this riddle, I said his name. What is it?

The first puzzle is not a question. It is a statement, saying that the word “what” has 4 letters, the word “sometimes” has 9 letters, and the word “never” has 5 letters. There is nothing to solve, so the puzzle is figuring that out!

The second puzzle actually reads as “There are 30 cows and 20 ate chickens. How many didn’t?” Thus, the answer is that 10 cows didn’t eat chickens.

The third question often confuses people and they pronounce TWO as [twou] instead of [tuː].

The fourth riddle actually says: “He tipped his hat, ‘Andrew Hiscane'”. Thus, the name of the man is Andrew Hiscane.

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